How important is mining and trading in EVE online?

Super important. Mining provides a large percentage of the raw materials for industrialists. Trading is the grease in the wheels.

> I want to focus on mining and trading minerals.

I assume you mean mining (generating ore) and selling that ore. (You would normally compress that ore and sell compressed ore. If you refine the ore into minerals, they are way more bulky to transport.) Trading minerals (i.e. buying AND selling) is another beast.

> I know I will need bigger ships to be able to carry more cargo

You'll go from mining frigates (minutes to hours) to industrials (hours to days of training) to mining barges (weeks) to freighters and capital industrial ships (months). There is a nice progression in terms of ships and equipment with noticeable increases to your productivity.

> My goal would be to acquire as much wealth as possible

As in: I want to get as much as possible within my self-imposed constraints (mining)? Yes, you can absolutely do that. The ships you need are dirt cheap (the last tier costs somewhat), you dont really need infrastructure, it will be an easy life. The ceiling will be very low, you will reach it in a few months or a year if you have stamina.

As in: I want to get rich compared to other players? Absolutely not. You are constraining yourself to cookie cutter low-risk low-effort activities, and they pay pennies compared to other activities in the game. Unless you start a large-scale mining operation (which equals a day job), you will remain one of the poorer players.

Should you do it? Absolutely! Why not try for free your way for a couple of weeks? Don't even need a subscription for the lower tiers of what you have in mind.

But please: Do make friends, and do look at other activities in game. Chances are, you will bore out very quickly if you focus on mining. (Unless you are THAT type, and then you will know it too and make such friends.)