A budget of $1000 is about 1 GPU probably a 1070 or 1070ti - with an old mobo/system or 1 GPU 1060 with a mobo, cpu etc. It would take you a while to mine a profit with 1 GPU. You'd want your own rig so that you can swap between algo/coins. You can def make a profit, but with that budget it would be a bit low.
1 GPU very difficult making a profit because profit mining related how much price electricity per kWh and every country are different. but mining can't get short time profit (ROI) except have surprise such Hardfork 1:10 or price a coin rise when to convert BTC.