In terms of load, the dual core Opteron is fine, the RAM is more than enough, but how much traffic are you anticipating/hoping/wishing to have? In addition, is your Win2k8 64-bit? Is SQL Server 64-bit? Have you thought about the potential security and performance issues having the web server and database server on the same box?
Again, without having all the information or particulars about your setup, if your web app (I assume it's only 1 web application) is just starting out and you're not anticipating a large load immediately, why not consider shared hosting first? It'll be cheaper (in the beginning) and most providers usually make upgrading easier to server hosting rather than going down from server hosting to shared.
But to get to your question:
I need a new dedicated server to host
my web app and am wondering what kind
of load (average requests per month)
this server could support.
If you're talking about static pages (cached preferably) with little to no database interaction. You could easily do hit 10k/min like mrdenny mentioned. I can't forsee any issues with taking that kind of load. Bear in mind some IIS7 tuning is necessary, but the hardware should have no issues in dealing with that.
Now if you're taking about one ASP.NET webapp with heavy database interaction and with a lot of performance tuned programming (app pool tuning, using partial cache, refrain from viewstate, using inproc sessions or cookie sessions, etc. etc.) I'd be fairly optimistic and say that ~250/min is achievable. I'd really like a little more explanation of what you're trying to do rather than the equipment you're planning to use.
Also, is $129 a month a good deal for
It's a little steep but I'm sure they have 24/7 support, high SLA uptime, redundant power available on-site, etc. etc. Personally, if the traffic isn't going to really be used and the server isn't really being utilized (~65%-70%+ utilization), maybe you're better off starting with shared hosting. Sorry to be repetitious, but don't spend all the money at the beginning. Most providers are helpful if you need to move from shared hosting to server level hosting anyway.