You should be able to get something, probably best go for used good quality than new bottom end stuff.
I had a Axminster m900 that I started and would be within your budget used. Axmister also make many similar other models that are all fine. Many swear by Record Power lathes, I must admit I'm not a fan but worth looking at (if you do end up with the RP m/c, go for the CL range with solid bed bars and cam locking levers, cheap / early ones had hollow tubes that were a bit light weight IMHO and the tool rest was moved and re-secured by loosening & tightening a nut / bolt - real PITA after a while!) . I would suggest avoiding the single tube lathes made by Clarke and others - they are really built quite poorly and will create quite a few frustrations.
If you could spare a day then I would still recommend a trip to the mill at Portishead, even as a one off would be a day well spent and I sure they'd welcome you for a trial day (need to phone/ email though as I think they get very busy to check space etc).
Also, have a look on the sticky posts above in this forum, one of they contains a list of the lathes owned by poeple on here, there may be someone with something you've seen to ask direct questions of.
If you're set of buying independently on ebay etc then look for the 'bundles' as they can be better value than buying individually.
A perfect package would include
Lathe
Woodturning chuck (and spare jaw set or two!) - key operated are easier than the two level system and I'd avoid the 'multistar' type of chuck with loose inserts and elestic bands unless you've got at least 4 arms.
Driver centre
Live centre
Tailstock drill chuck
Face plate
Tools (HSS) - good starter sets are prob roughing gouge, spindle gouge, skew, bowl gouge, round nose scraper, parting tool. Rest can come later. Gold star for makes like Henry Taylor, Sorby, Ashley Isles, Crown, Axmister.
Finally Keith Rowley's book on intro to turning is generally regarded as the definative beginners' guide and is well worth buying. Other 'book' to own is the Axminster catalogue, FoC and very useful to give you the idea of what is out there even if your looking for used.
Hope that helps, all my opinion of course but such are internet forums!
Simon