the best place to start is the library and petshop. Get some books out from the library and look at the fish in them. Check out the fish at your local petshop and make a list of what you want to keep. Once you know what fish you want, you can look for a tank that is suitable for them.
If you do a fishless cycle it will be about a month before you can add fish to the tank. If you do a fish in cycle, then you can add fish within a few days of obtaing the aquarium. However, a lot of fish don't do well in a tank that is cycling (developing the good filter bacteria) and most people end up losing a few of them during the process. It also requires a bit more work to do a fish in cycle as you will have to do partial water changes once a day or every couple of days. If you do a fishless cycle you only do a water change after the filters have developed.
A second hand tank is fine. The advantage of buying a new tank is it should come with a guarantee not to leak. Second hand tanks might be starting to leak a month after you get them, or might last 20years before the silicon comes away from the glass. The silicon is the glue that holds the glass together.
New tanks will also be clean and free of disease. And they won't require as much cleaning before you can use them. However, if you find a second hand tank that is still running with fish in, and has been maintained properly, you could simply drain it and move it to your house, then set it back up. One instant aquarium
Personally I prefer to buy new tanks & equipment, but I am just paranoid about bugs and germs
If you do get a second hand tank look at the silicon between the glass. It should be either clear or black in colour (there's two different colours of silicon used in fish tanks) without any bubbles in. There should be no white or cream patches in the silicon. And when you touch the silicon it should be firm but slightly flexible. That is to say you can push on it and it should move a tiny amount, but you should not leave an impression in the silicon. Also you should not be able to pull the silicon away from the glass.