1 per Tile to start with, Starbase modules Increase this to 2,3,4 & 7.

Once you mine and have it. It will show in your User interface at the top of the screen. From there you can build ships which require that resource. One ship per resource but if the ship is destroyed you get it back. 

For example if you have anti matter you can build a proto-type small missile boat with an attack value of 20 or something like that. Your anti matter will then show as ZERO but you will have the small boat to show for it. 

Or you can trade it to other Ai/Factions for whatever, money or tech. Again your resource will list at zero. You can mine both archaeology and mine-able resources if you have the modules added. 

They are definitely worth getting early on. Some of the later game modules make the weapons very powerful, the Shield Punch for Beams is down right overpowered and one of the modules I equip on heavy battleships. Because I like Elerium so much I set my Galaxies to have 'common nebulae' so there are more of them.

It depends on how your faction is. explore, war, etc

Then what is available first.

What type of weapons and defenses will be best. Use diplo to see what potential enemies have.

There are so many combos the best thing may be to just try MANY dif combos to see what is best for when.

there are planetary buildings that require upgrades

and you can design ships that take multiple resources as well

some ships that might take 2-3 antimatter or even 2-3 of several different types of resources

also if you have mercenaries many of their ships have a resource cost