At that sort of price range, I'd guess you're mainly going to be looking at second hand.
Any of the big name manufacturers (Specialized, Trek, Giant etc) offerings are going to be pretty decent, Age and condition are going to be more important. The only ones to be wary of are the bottom feeder manufacturers selling through
Ebay/ToysRus etc. Typically these will be new bikes with 14/16 spd gearing, Hi-ten frames and no-name components made from cheese.
With a bit of careful searching you should be able to turn something up in a decent make with 18spd Shimano gearing (look for Sora or Tiagra groupset) This will give you shifters integrated into the brake levers and it will be relatively easy to obtain replacement parts as needed. If you live in a very hilly area you may well want to look out for a compact (50/34 chain rings) or a triple, rather than the standard 53/39 doubles fitted as standard a few years ago.
There's nothing wrong with downtube/friction shifters but they will normally be fitted on older bikes, this may not be an issue, but unless you know what you're doing you could easily end up with a dog.
New bikes are available at the top end of your price range. The Carrera range from (hawk, spit)
Halfords has a decent reputation, as does the
Decathlon btwin sport range. Only thing with new bikes is you'll obviously get a lesser spec for your money.
Main thing with any bike, is to make sure it fits before you buy.
