.177 is ideal for target shooting with it's virtually flat trajectory over 7-35yrds and is what all target shooters use. For your money it'll either be spring powered (either break-barrel or underlever) or CO2 which will be bolt action. I wouldn't bother with CO2 as it's extremely difficult to get any consistency when using CO2 without spending money and modifying the crap out of it (been there/done that).
For pellets I'd go with either JSB Exacts (they come in 3 minutely different sizes of .177 to match your barrel exactly for best accuracy) or domed Accupells.
For your budget I'd look at either a SMK, XS or QB (all chinese makes) break barrel if buying new or, if can find one, a Cometa or BSA lightning 2nd hand. SMK aren't amazing but will do the job.
Scopes again are limited by your budget but TBH as your not hunting any £20 3-9x40 or £5 4x20 off ebay will do to start with.
TBH I'd look at the 2nd hand sales on boards like
www.airgunbbs.com as you'll get more for your money as well as being a very good source of information as well.
If you want to shoot in your back yard read up on the Air Rifle laws very carefully before you get a knock at the door from some very irate armed police after a neighbour tells them about the gun wielding maniac who lives next door!
My very varied history has most things from £100 to £1800 rifles - .22 CO2 AirMagnum 850, .22 Spring Cometa 400 .177 PCP Logun Solo, .177 PCP BSA S10 Mk3, .177 PCP Daystate Airwolf, .22 PCP S200/BSA Ultra Hybrid, .22 CO2 QB78. For scopes I've used everything from £20 off eBay chinese 4x20's to £300 MCT target scopes to £1000 digital night vision and everywhere inbetween.