I will echo some sentiments; the bass you should buy is the bass that feels best in your hands.
Here are some tips from a Bass Player magazine article on the topic of buying a bass:
If you have a bass that you can use indefinitely (i.e. borrowed from a friend, cheap starter bass), keep it around until you can save up to buy your dream bass. Having an instrument puts you a little ahead of the game in that you have a point of reference; you know what you like about that instrument and what you don't like, even if you may not be able to express it in words, and even if you don't consciously know you like or don't like it. It also makes budget less of a factor; no matter how bad the bass is, it's a bass you can use, allowing you to save your pennies.
If you don't have a bass yet, or are losing the use of someone else's and have to get your own, then budget is a factor. Figure out what you can afford to spend, and don't look at anything, no matter how drool-worthy, that isn't in your price range.
If this is your first bass, don't break the bank. Your first bass is something to get good on, and to use to decide that you want to pursue the bass more seriously, before you drop $5,000 on a high-end custom rig that doesn't do what you want and is difficult to offload. You can get quality gig-worthy instruments in the $500 range, and giggable amps in about that same range, that will last you more than long enough to decide where you want to go from there. Once you have something better, cheaper instruments are easier to sell on the used market, and you'll take less of a loss than trying to unload a high-dollar one-off instrument nobody else wants.
The absolute most important thing you should look for in a bass, especially a first bass, is feel. It should be easily playable, and comfortable to play. While learning bass involves a certain amount of discomfort as your fingers learn how to stretch in odd ways and your fingertips toughen up, believe it or not most of a new player's pain is an unnecessary result of an instrument that doesn't fit the player. There are many subtle variables in how a bass is designed, such as neck shape and thickness, scale length, string spacing, body size and shape, instrument weight and balance, positioning of controls, etc that can make an instrument a bass player's dream or nightmare. The difference is often from player-to-player as much as from bass to bass; one guy might find a 36" scale 5-stringer with 21mm spacing the easiest thing in the world to play, and may hate a narrower-spaced long-scale four-stringer that is another player's perfect fit.
Related to but slightly separate is the adjust-ability of the instrument. There are things you can't change about an instrument (mostly mentioned above as part of "feel"), and things you can. Individual string height, neck curvature, even string spacing (depending on the type of bridge) can be adjusted to make an instrument a perfect player or a complete wreck. This is again subject to some player preference; a newbie might like a slightly higher action to prevent fretbuzz caused by overenthusiastic plucking, but there's a bell curve for these settings that most players prefer, and a new player should probably fit somewhere in the middle third. Be careful when thinking something can or can't be adjusted; a used instrument may have a broken truss rod, or it may be at the maximum, and you wouldn't know unless you brought a toolkit to the store and set each instrument up yourself.
The next most important thing is sound. If the bass doesn't sound good, you won't want to play it. There are some adjustments that can be made to alter a bass's sound, particularly in the choice and settings of the amplifier, but you generally want to start with each knob on the bass either in its center detent if it has one, or all the way up if it doesn't, and each knob on the amp in its center detent if it has one, or all the way DOWN if it doesn't. Plug in, switch on, and turn the volume on the amp up to an agreeable level. This should be a "good" sound in your opinion, and a few minor tweaks to bass or amp knobs should result in a "great" sound. You shouldn't have to crank any EQ knob to either extreme, and you should be able to get a "great" sound from ANY bass. If you don't like the sound, don't buy the bass.
The absolute LEAST important thing, especially on a new bass, is looks. If the bass feels good, plays good and sounds good, but is pink sparkle with rainbows and butterflies, it goes on the shortlist. At the very least, you can buy that bass, hide it in a gig bag while in public, and take it to a luthier who can refinish it in any solid color you choose. What's more likely is that the store will be able to special-order the same model of bass in a different color, and unless that company is infamous for lax QC, you should expect the same feel, playability and sound out of the instrument (some chain stores will special-order most any factory-built instrument with no obligation to buy, so if the one they order you turns out to be a dud you can say no).
When looking for an amp to go along with your first bass, the first thing to consider is what you'll use it for. While you're learning and doing basic exercises, a "practice" amp, which is a combo amp somewhere between 10 and 100W, will work just fine for practicing scales, modes, arpeggios, and general jamming to CD tracks. It may even work for low-volume practice with bandmates. However, amps in that class probably won't stand up to the rest of your band's "gig rigs". This is for several reasons:
First, tube amps (preferred for guitar) react differently than solid-state (generally used for bass and PA). Tube amps are rated for the maximum wattage that produces a "clean" output signal, but you can push a tube amp harder than its rating and get more volume. A solid-state amp pretty much maxes out at its upper rating; if you push a solid-state amp into distortion, you get a distorted sound at the same maximum amplitude as your loudest clean tone.
Second, that's exactly what your guitarist is probably doing if he's overdriving his amp. Guitarists want to run out of headroom at a particular level, so they can get natural tube overdrive out of their amps at "performance" levels. You as a bassist NEVER want to run out of headroom (at least for most music styles). So, you need wattage that can reproduce your bass's clean tone, cleanly, at the necessary volume to compete with a distorted guitar amp (or three).
Third, as the frequency of a sound decreases, the perceived volume of that sound also decreases; that means you need more power for more real volume in order to sound as loud as a guitar, even if the guitar's clean. A guitar amp is tuned to produce middle and high frequencies relatively efficiently; you need those same mids and highs, but you also need earth-shaking lows in order for it to sound like there's a bass in the mix.
All of this means that in order to be present in the "stage sound", your rig needs at least half again the combined wattage of the rest of your band's rigs. To compete with a single 30W guitar amp being run cleanly, you'll want at least 50w of bass amp. If you have a second guitarist with the same rig, you'll need about 100W. The harder your guitarists push their rigs, the more power you'll need; if both guitarists are overdriving their rigs, you'll need 250W. A metal bassist competing with 2 50w guitar amps in full distortion, a 100w keys amp and a kit drummer might need as much as 600W worth of rig.
At some point, it becomes impractical to try to compete. If you reach that point, ask yourself and your bandmates if they really need to have that kind of power. 100W full stacks are what you bring to a stadium gig, and even then I've seen stage managers unplug one of the two cabs and mic the remaining one to send it through the 5000W PA system, so the guys in the cheap seats can hear without clearing the front rows.
Something to keep in mind is that double the head power does not equal double the volume; a 20W rig, all other things being equal, will only sound just noticeably louder than a 10W rig. It would take 100W to sound twice as loud as 10W. Adding speakers to a smaller amp will actually get you more volume than doubling the power, because while the speakers each get less power, there's a law of diminishing returns as to how hard you can push a speaker, so doubling the speakers, and thus halving the power to each speaker, does not halve the SPL produced by each speaker. Four speakers will produce significantly more sound with the same watts than two. Of course, more power AND more speakers is best, but if you're getting drowned out, consider making that half-stack a full stack with the same amp head, or adding an extension cab to that combo; you may be surprised.