You can use this build, it's within your budget and it's a solid one. You'll have no trouble with it. Iof yu want to, you can remove de SSD to fit exactly in your $1000,00 budget, i'd recommend spending a little more to get it tho.
Are you planning to build it from scratch or do you have any piece remaining?
Oops...I Didn't mean to pick this as solution
Im going to build it from scratch
Hmm, okay. So you can go with that ^^ It has everything you need already.
If you had some pieces remaining we could add more powerful pieces, but as you stated, it's from scratch. Within that budget, i believe this is a very solid build.