I agree with Vipitis (and thank you for your kind words).
Most of my cameras are not intended for precision thermography, which makes them much more affordable. But resolution and lens choice are vital.
You can get good results with a 320 x 240 or 384 x 288 sensor, which is roughly the same as a VHS video tape (remember them?), which the market considered acceptable for moving images for years. Using superresolution (shaky hand) techniques can improve on the effective resolution by up to about a factor of 1.5 or 2; multiple exposures (pan and scan) can give you extremely high resolution of a fixed subject, provided your lens is capable of breaking the subject down into small chunks. Think in terms of visible-light gigapixel photos made with a camera on maximum zoom.
Higher resolution sensors can give sharper results. The 640 x 480 class is very nice, although if I could afford it I would definitely buy an XGA (1024 x 768) or SXGA (1280 x 1024) sensor. I'm hoping that the new generation of sensors from China may make this possible in the next several years.
The right lens - or interchangeable lenses - make a difference, too. Wide- or narrow-angle lenses need to be chosen to suit the subject. I would love to have one of the 25-250mm (class) motorised zoom lenses that are out there, but they remain well beyond my pocket. For general looking around a short focal length (eg 6.8mm) works fine but for detailed work a longer focal length is very useful. Also, if you have more than one lens you can combine them for microscopy and similar work.
Most of the time I find I do my thermal work in black and white, although I have managed some pleasing images in false colour. Vipitis is right, that one can do a lot in post-processing if you choose. I tend to use ThermViewer with my Therm-App cameras, because (a) it gives decent results and (b) outputs a data file of the actual values of each pixel. I haven't started using these files yet but I figure they're a kind of insurance: I have rescued several visible light photos courtesy of the RAW files, and I suspect I will have the same latitude in the future with the thermal equivalent.
Frame rate is an interesting concern. I find it much easier, and quicker, to focus my 25Hz Therm-App cameras than their 9Hz brothers. Trying to maintain good focus on a moving object is quite difficult with a 9Hz frame rate.
That leads me on to focus. If you are considering using a thermal camera for 'photographic' purposes then adjustable focus is a must, which narrows the choice of devices. Any number of thermal images that would be very attractive are, in my opinion, ruined by the poor focus - either due to the limitations of the device, or because the operator didn't really understand what they were doing. Despite the remarkable things that one can do with software, sharpness really cannot be dialed-in in post!
Cost of hardware is the big stumbling block for most people, me included. I would recommend putting money into the best sensor you can buy, along with a single middle-range lens, with the idea of getting more lens options later. The smartphone 'dongle' thermal cameras generally offer good value for money, but don't have quite the same performance as the research-grade imagers. For 'photographic' use I would usually choose more pixels over accurate thermography - but at the same time it's really important to make sure the camera has good noise performance. Granted, noise reduction algorithms can help, but - as with focus - you're always better off getting the highest possible quality in the first instance.
Finally, don't forget that whatever equipment you may or may not have, image composition is key. I know I have made (and published) many badly composed images but the basic rules of composition work just the same whether you're working with paint, pencils, photography or thermography.
I know I've rambled on, and I'm sure many others will be able to add their wisdom in far fewer words. But if anyone wants to discuss thermal photography privately, I'm happy to do so via PM and thence email.