If you want a true 1000+ yd rifle I would look at cartridges like the 300 RUM, 338 RUM/Lapua/Edge. The easiest two on your wallet will probably be the 300 RUM and 338 RUM and are both as about a good all around rifle as you will get. My first recomendation would be the 300 RUM. You can get them in the factory Sendero platform which is usually a great shooter right out of the box - am very happy with mine. HS aluminum bedded stock and heavy varmit Sendero contour barrel. When your barrel burns out you have a great platform for a rebarrel build.
The 375 RUM comes up a little short for 1000 yd hunting because of the lack of high BC bullets available (i.e. 260 AB), which run out of velocity down range. I've seen in some other threads that there are some wildcat/custom bullets available with higher BC's. The 300 WM also comes up a little short of 1000 yds with most bullet/load combinations. The 300 RUM will get you about 300 fps more velocity than the WM which is good for about 250 yds more range. On barrel life you can probably expect about 1000 rounds out of the RUM and 1500 out of the WM if shooting max loads.
If your interested in the 300 WM, you might consider the 300 WSM
which is very close to the WM in performance, and in fact I can get better performance than a WM from my WSM using RL17. The 300 WSM has much longer barrel life - up to 4000 rounds.
A good 30 cal bullet that will make the 300 WM or WSM 1000+ rifles is the GS HV 177. They have a very good BC and will shoot faster than other bullets. They are also spendy and must be ordered from S Africa.
Hope that helps,