If your budget is really only a grand, that limits your choices.
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Budget is not problem. It's just minimum budget. I can invest in mining upto 3-5k USD. I also have 2 PC of 2 GB RAM and I am going to buy new one for mining purpose only.
Asic miner works only for BTC ? not in other coins?
Which miner will be best for DASH?
trading I hate. I don't have time for trading.
OK so build a PC with a low power CPU, 4GB ram, a very small hard drive and a very large gold rated power supply. Install Linux or Windows based on what you can manage easiest. Install a couple of high end video cards and go for it. I would suggest installing the legacy version of NiceHash to get started mining some coins. It will balance between different coins depending on what is earning the best at the moment. Once you get more experience you can try to mine directly to the coins of your choice.
If you want to invest a bit more money, buy riser cards for that same PC and add 3-4 more video cards. I'd suggest sticking to the same brand of GPUs (Either NVIDIA or AMD) to avoid issues. If you really want to mine a large variety of coins, the Nvidias might be a better option. 1070's were mentioned which work very well but try not to pay too much for them as they cost more than normal at the moment.