No scope that you can carry will allow you to reliably see bullet holes fired from non-crew served competition rifles at 1000 yards.
For competition, you will need a spotting scope through which you can see the scoring disk and the shot marker and anything around 10-20X will do fine for that. No need to get higher magnification, that's what your riflescope needs to be able to do. The other use you will have for that spotting scope is for observing conditions and here you want more field of view than high end magnification, so again a 20some X scope is all you need.
Eschew the calls of "buy once, cry once." This is not needed here and new models are coming out all the time. I would say that something around $3-400 is going to be plenty to start with. Look at low end Nikon, Leupold, Konus, etc. Stay away from Barksa, NC Star and other similar sold at Wal-Mart in plastic bubble packaging.