I am not looking to reproduce synth sounds of the analog moog variety, but rather to emulate various instruments that might be in a pop, rock or country or folk music band.
I suggest either a physical modeling synthesizer or multisample synthesizer designed to reproduce classic keyboard sounds. Something like a used Nord Electro 2 (around USD 1000 on e-Bay), which is actually a hybrid of the two types I recommend, is a perfect example.
As I mention in my comment, it's not so easy to find good non-keyboard sounds in a keyboard instrument. The best non-keyboard sounds tend to be orchestral ensemble sounds (a strings section or brass section), then maybe electric bass sounds, acoustic bass sounds, and drums and percussion. I've never heard a decent guitar, banjo, mandolin, ukelele, or other plucked instrument sound. I attribute this partly to difficulty in reproducing the raw sounds themselves, and also to the difficulty in re-creating the actual articulations of non-keyboard instruments using a keyboard.
Of course, re-creating keyboard articulations using a keyboard is dead easy. Acoustic piano is an instrument that is used for almost every purpose in literally every genre, so having one of those around is always a good plan. It's not so obvious how common it is to hear electric piano sounds in all kinds of rock, pop, country, R&B, etc. It's a subtle sound but it's also very versatile. The Hammond B3 organ is an excellent and versatile "pad" sound and also comprises most of the "bass" sounds for the band The Doors. So those are the sounds I would look for.
Physical modeling uses digital re-creations of the individual components of a device that are virtually connected exactly like they would be in the real device to create a very good re-creation of the sounds and response of the modeled device. This is a good technique for reproducing the sounds of a tonewheel organ like the Hammond B3 by using samples for the sounds of the individual tone wheels and then physically modeling the playback, mixing, and effects characteristics of the rest of the electronics of such an organ.
Multisampling uses multiple samples of each note of an instrument at several levels of playing intensity, and even uses multiple samples of the same note at the same intensity (that are then randomly selected from on playback). While it can be memory and computing intensive, multisampling is extremely effective at reproducing acoustic and electric piano sounds, since the entire sound of each note is determined by the stroke of the hammer, and the only "articulation" available after the hammer has struck is the dropping of the damper on the string or tine.
Note that if you are using a DAW, many of the best synthesizers are actually software plugins. For instance, currently the best acoustic piano synth I've heard is Apple's Steinway Grand sample for their ESX sampler, available in Logic and Mainstage. If you want to go with software synths, the choices are endless, and all you'll need otherwise is a good controller. I'd recommend finding one with USB bus power, and decide carefully what kind of action you want (fully weighted, semi-weighted, etc.) based on your comfort level and how you like to play. Many controllers also have knobs, faders, buttons, and pads that can be mapped to software controls to bring synth settings out to the hardware. That requires mapping of the controls and normally those controls aren't labelled the way the would be on a dedicated keyboard synth. The upside to this plan, if you already have the computer and the DAW, is you can get a decent controller for much less than $1000 and you can add on additional software instruments as needs arise and budget allows.
