The big question I have is: is this an electric or acoustic guitar? The suggestions answers to these questions depend an awful lot on what kind of guitar you have.
Do broken strings damage the guitar in anyway
Not at all. Think of changing strings as an oil change; something the device is built to have happen regularly.
(I)s it recommended that I remove the broken string before the new ones arrive.
There is no good reason to keep broken strings hanging off your guitar. I would find it a disincentive to practice. I would finish a song and maybe a set with a broken string hanging off, but would change strings first thing after. But the guitar doesn't care.
Do I have to replace all the strings or just the broken one.
It depends on context. For me, I often go months if not years on a set of strings, and my strings break on metal fatigue. Thus, when that happens, I figure the other strings have lost their bloom and are not long for this world, so I change the whole set.
If I broke a string while putting the new set on, I would blame either my ear or tuner for telling me to tighten too much, or the manufacturer for making bad strings. In that case, I would likely get a new single string rather than replace the whole set.
What tools/resources would I need apart from the strings, considering that I am a complete beginer.
For most guitars, you should be able to change strings without anything but your hands. Wire cutters are useful for electric guitars, so you don't have to snake strings that have been bent around your tuners through the bridge, and to trim excess strings when done, but are not necessary. You can also use them and a small paperback to pry out the bridge pins of an acoustic guitar.
If you play a guitar with a locking nut and bridge, such as guitars fitted with Floyd Rose tremolo systems, you will need Allen wrenches and patience.
I also suggest you get an electronic tuner. There are many inexpensive ones that clip onto your headstock. There are some that run in your browser or on you smart phone. The problem, likely the reason you broke the string in the first place, is that your ear does not know what the high E string is supposed to sound like, so you tightened it too tight. I know I went through high E strings all the time as a beginner. Systems like tuning forks or pitch pipes, which require you to listen and compare two notes, are no good until you have a trained ear.
Any suggestions on what kind of strings to buy.
My suggestion for beginner guitarists is to get medium strings from a reputable brand. If you've seen a set of strings advertised in a guitar magazine, that's safe for you. Eventually, you might decide to like brand A over brand B, but you have to get yourself beyond a beginner stage in order to tell the difference.
Similarly, there are guitarists who swear by heavy strings. Electric players will tell you they stay in tune better and give more tone, and acoustic players will say the greater mass allows the instrument to project more. And there are guitarists who swear by light strings. Electric players will say you can bend more and you should leave it to the amp to give you power. What you choose goes to what kind of guitarist you end up being. Right now, medium strings -- somewhere about .010-.046 for electric, .013-.056 for acoustic -- is what you want. If your fingers hurt, you're squeezing the notes too hard and need to develop a lighter touch; that's not the instrument's fault or the strings' fault, it's on you.
Rules of the forum discourage suggesting particular brands, and even if I was to have strong preferences -- I have preferences, but they are not strong -- I wouldn't post them here, because what works for me might not work for you. Guitarist X plays Y strings, and they work for X, but I don't have X's rig or X's gig. My best suggestion: Play medium strings with a medium pick until you can express a reason to change.
