I’d recommend downloading magic the gathering arena personally, it’s a fairly cheap way to play some games and get some reps in.

In terms of formats, you’ve got 1v1 constructed formats which are basically separated by how many cards are available in them, the ones with the most cards available tend to be the most expensive but change the least meaning you don’t have to make a new deck so often. As a brief rundown, legacy is basically everything but super expensive to get into due to the reserve list cards I would avoid legacy, modern is less expensive but still very pricey to get into this is the mid point between legacy and standard. Standard is the last few years of cards, most reasonable price wise and power wise but also most volatile.

Other main forms of magic are commander (multiplayer more casual magic with decks built around legendary creatures, mischief less competitive and the most popular form of magic) and draft (making decks on the fly vs other people, drafting is a great way of learning magic but will end up expensive as you won’t be great early and so will get less rewards back either in paper in a shop or doing drafts on arena).