It all depends what sort of shooting you intend to do with it.
A semi auto is good fun on the range and a fully tricked out Ruger 10/22 may be reliable and accurate but we are talking a lot of money to bring it up to scratch. IMO there are no reasonably priced semi-auto .22 RF that can compare in accuracy and reliability to a bolt action. You will be using subsonics for hunting and these can be a little underpowered for the purpose of operating the action when it's had a few rounds through it and gets dirty. It is also a rare semi that can do better than 1" at 50 yards out of the box. Your limit for range is the range at which you can consistently put your rounds in the kill area of your target, in this case about an inch.
In my opinion the most important attributes of a hunting rifle, be it for rabbits or dangerous game, is reliability and accuracy.
For a pure bunny gun, one that will be used in all weathers and purely as a tool it's hard to beat the CZ or earlier Brno bolt action rimfires at any money IMO. There are higher quality, better finished rifles with better triggers but the CZ or brno is tough, accurate and reliable.
If you have a look on guntrader:
http://www.guntrader.co.uk/ and do a search for .22 on there.
A quick search shows a few nice Brno model 2s and even a couple of more recent CZ 452 for under 200 quid. A .22 is almost impossible to shoot out so as long as it's not abused even the older Brno Model 2s should have tens of thousands of rounds left in them and to be perfectly honest are probably much better built than the more modern offerings.
Make sure you get a couple of magazines as the actions stops when you run out of rounds.
Also make sure that it's screwcut ( Threaded for a sound moderator), you did apply for a sound moderator didn't you?
A Parker-Hale moderator is nice and traditional looking, if the barrel has been chopped very short then a bit of weight from the steel unit can help with restore some of the the balance. Another popular moderator is called the "SAK" and being aluminium is a bit lighter. These get dirty on a .22 and so are both strippable. Both are around 30-40 quid, no need to spend more with subsonics.
If you get a CZ the trigger is likely to be as rough as a badger's fundament. Buying second hand you could get lucky and find that the previous owner has had the trigger fettled to a nice crisp, light release but if it isn't a kit from this guy :
http://www.yodaveproducts.com/ is around a tenner and transforms the trigger.
In terms of ammo the two main brands seem to be Winchester or Eley subs. The Winchesters have bigger hollowpoints and seem to hit a bit harder at range but the difference is marginal and you should shoot whatever is most accurate in your rifle.
Any questions, shoot.