First of all if you want to mine gather all the information that you need like what coins will you mine. For example if you would mine Bitcoin you can use an ASIC miner. Mining Altcoins the use a GPU mining setup. There are also altcoins that are minable by CPU if you want. If you are set in what cypto you want to mine then go build your mining rig and if you are going to mine with either an ASIC miner or GPU just keep the other specs of you rig to the best back to you buck component and invest on a capable CPU. For GPU mining I recommend the RX 570 and the GTX 1060 to be the bare minimum. If you will be CPU mining the go for the Ryzen 5 1400 or the i5 8400 however of the later good luck on finding it right now since the stocks are scarce and it does not have a cheap motherboard to pair to right now.
I mean like 3/4 HD7970 as an example. These cards are cheap. Is it possible to make some profits with these cards ? (could be a cheap way to start mining)
I'm not going into mining but I would like to know ...
You can you those cards however consider your electricity bill this cards are power hungry with the TDP of 300w. Also it is beaten by the RX 570 by 23% with a lower power consumption(just a TDP of 120w) so better go for the latter GPUs if your electricity is not free in your area.