Start with what I did: Do your homework, and double-check every option available to you before you make a final decision. It usually helps to set yourself a budget, then look for machines that fall in that range.
That being said, by asking here, you took a step that I wish I had: reaching out to others for their opinions. This forum contains experts and newbies alike, so most of the time you might find someone who has made similar mistakes, or someone who can help you prevent one from happening.
Back to your initial request: A great place to get an idea of what exists and what to look for (in terms of the name brands) is the Make: Magazine 3D Printer Buyer's Guide. These guys have been keeping a spotlight on 3D printing for a long time, and may even inspire you to put your new printer to use.
The site I bought mine from: https://www.3dprintersonlinestore.com/
It is based in Asia, but the shipping is free, unlike most of the other cheap alternatives I found at the time. They sell both name-brand and clone printers, and while they do sell stuff like [shudder] Sintron, they also have the reliable stuff like Folgertech. If you do check the site out, be sure to look up the actual brand, and see if they have a website (Folgertech does). While I expect buying direct is too pricey to ship, but I just checked the shipping for a MaxMicron printer to Bristol, UK...4-6 days DHL shipping, $0. I'd assume the same applies to all of the other DIY printers (to anywhere in the UK), if not all of the printers.
But that's just where I got my printer. What really matters is, which printer do you want? Are you looking for the closest a printer can get to Plug-n-Play, or can you get your hands dirty? Are you satisfied with a portable machine meant for PLA, or do you need a large machine that can print ABS?
Don't make the same mistakes that I did. Think about what you want, look at the machines that offer just that, research these machines to see what they need, and double check that what you are about to buy is right for you.
Oh, and listen to the other posters:
XYZ printing=bad, unless you want to see how cheap a "name-brand" 3D printer can be (I know, my school has the original).
Acylic frame=also bad, my printer at home has a few pieces mixed in and the most critical ones all broke
Start with a Cartesian (basic x,y,z coordinates). Deltas and h-bot gantrys are harder to maintain and work best with powerful 32-bit controllers that can handle the complex calculations required. Cartesians and some others can get away with 8-bit AVR controllers, like RAMPS.
If some of these terms go over your head, Google them. It's good stuff to know.
Filastruder 2607 w/ Filawinder @1.75mm.
Dual-extruder MaxMicron Prusa Mendel: RAMPS 1.4 w/ Repetier Firmware+Full Graphic LCD Controller, stock hotends, 3Dator extruders w/ MK8 gears, insulated enclosure w/ 2 heat lamps, RPi 2B w/ Repetier Server.
0.1-0.2mm layer height, heated bed w/ PEI surface, inductive-sensor autolevel, 0.5mm to 0.2mm nozzle diameters.