We can help a little, but we cannot make the decisions for you, you will need to decide that for yourself. It will be tough to stay under that price point but it is doable. There are way too many choices to just give you a list of parts to buy. You need to make a decision on 4s upt to 6s for batteries since that will change the motor KV and what the ESC's need to be rated for etc.
If you want good parts with a good customer service aspect, look at RaceDayQuads and think about these parts...
Too many stacks to pick from, all of them work, and all of them can have failures, so it isn't an easy choice and there are no guarantees even if your soldering and electrical knowledge is good.
You will want a full size camera unless yo want to mess with getting 3d printed parts to make a smaller camera fit. Look at a Foxeer Falkor, but again, too many options to pick from for us to say which exact one.
If you want to get real cheapy on your build, you can watch this for your build. It's a couple years old, but newer than the first version, so not sure if some of the links to get parts are still available or not. See what you think.