I am setting up my first turntable. I
Music Hall turntables are made in the same factory as Project, and some models from each line (they are separate lines) share the same parts - arms, for example. Both offer great value at a number of price points.
I've had an MMF-7 for years and continue to be very happy with it. I don't think there is an appreciably better TT on the market for less than twice its price. My preference, if limited to the alternatives you give, would be the MMF-5 - a very highly respected turntable/cartridge combo that might very well please you for years to come. I'd pair it with the fine sounding Bellari Tube Phono preamp which sells for the bargain price of $250 and spend the rest of the budget on music - there are lots of great vinyl reissues waiting for you.
Should you feel, however, that you want to make a more limited investment now to see whether you really get bitten by the vinyl bug, I'd recommend the Rega P-1 at $350. At virtually the same price, it is a better value than the Project you've been shown. Pair it with the Bellari and you can be spinning LP's very nicely for about half your projected budget.
Best of luck, and let us know what you decide to do.