While I can't condone shooting birds just for the count, I enjoy air guns so much that I can't not chime in here.
In general, a break-open barrel is not going to be as accurate as an under-lever or side-lever rifle. The 1000fps claim is made using the lightest possible ammunition in .177. You'll most likely want to use heavier ammunition. For birds, .177 is sufficient. If you're wanting anything larger, go with .22. And, speaking of pellets, buy good ones. They're worth the extra money but are still fairly inexpensive. You don't need match grade, just avoid the Crosmans from K-Mart.
If you buy a spring-piston rifle and put a scope on it, make sure it is a scope rated for air rifles. The Talon that MrSD pointed you to has its own air resevoir--one that you will have to recharge. This are usually quieter than springs, but also heavier and you do have to recharge them. On the plus side, they are often adjustable for velocity.
For a basic air gun, Gamo is good, but they do have some shortcomings. If you need a repair, they are the only ones who will work on them. Their trigger is not very good. They claim to be a two stage trigger but it isn't and it is very easy to strip their adjustment screw.
Consider Beeman and RWS. Both Beeman.com and AirGunExpress offer demo rifles for sale so you can usually get a pretty good price on one.
Sorry that I can't say anything about the Remingtons.
Hope this helps. Try not to shoot your eye out.
