There are a lot of really good quality air rifles out there. I know the RWS 34 is quite popular. I had one in .177 a while back that I picked up used and eventually traded it off. It seemed to have a lot of spring buzz to it. But, as I said I picked it up used so who knows what the whole story is on that particular rifle. I sold it to a friend of mine and he is quite happy with it and seems less bothered by it's buzz.
As far as caliber is concerned though, I've had a good number of various rifles in .177, .20 and .22. The game that I've hunted most with air rifles has been squirrels followed by rabbits and various pest birds. I've found squirrels to be noticeably tougher than rabbits and birds. Everything within reason has been effective on the rabbits and of course, the birds but I've found the .177 to be the all-around best on squirrels from both a quick kill and a flat trajectory standpoint. I agree with g.willikers that the consensus among "experts" is the larger/heavier pellets are better for hunting. However, I will say that .177 has been the best for me on Squirrels. At least this has been the case among typical air rifles in the commonly available power levels of around 900-950 in .177 springers, 700-750 .20 cal Sheridan, 750-825 in .20 and .22 springers. For game larger than squirrels and rabbits I have usually moved up to a 22 rimfire rifle so I can't offer much advice there.
If you're not already aware, I would caution against paying too much attention to advertised velocity claims in general and especially those that utilize aluminum, zinc alloy, type pellets. I use lead pellets and have choreographed every air rifle that I have owned in the last 25 years. Chronographs can be real eye openers and have shown that 90% of the "high performance," "adult" air rifles in the $150 - $250 price bracket fall into the above power levels regardless of advertised claims. I have had limited experience with the newer nitro piston rifles so I can't comment much there other than to say that they are very smooth.
As far as scopes are concerned, by one intended for air rifles and use some type of recoil stop and you won't have problems.
As to range, you hear a lot on the internet of extreme range, one shot kills. I suggest that you employ a pretty fine filter here and take them for what most are, flukes and/or fish stories. Most air rifles don't have a lot of excess power to work with and with respect towards the animals I hunt I try and keep the distance to around 30 yards or less.