Choose a format you want to play wisely.

Limited (draft) doesn't require any initial investment, but is expensive over time. Also it is probably the hardest to master. Expect to spend 10-15 per draft.

Standard is the most widely played competitive format. It is rotating, so whatever deck you buy now, you may have to replace partially or completely every 3-6 months, so it can also be expensive over time. For budget decks see articles and videos at http://www.mtggoldfish.com/series/budget-magic and videos by Nizzahon https://m.youtube.com/channel/UCkfWtgQSg3yp7vmIj3Z5W0A/playlists?shelf_id=12&sort=dd&view=50. Expect to spend some money every 6 months when metagame changes.

Modern is not rotating, so it is more pay once, play forever. The problem it is already too expensive to enter, and the most played cards are not in print anymore.

Pauper is also not rotating, and even the best decks don't cost too much. Unfortunately, it is less popular. If there is a Pauper playgroup in your area, it is definitely a solution to your problem.

Finally, there is Commander. A multiplayer format with 99-card decks. The format is also non rotating: your deck stays playable forever. Only one copy of every card can be played, it helps with the budget. The nice part, there are preconstructed decks to start with. And you can upgrade them one piece at a time whenever you can afford it.

Finally, I have to mention Magic Online. Playing some constructed formats, in particular Modern and Commander, is much cheaper online. Pauper is also very popular online.

Then, there are Magic Duels. Magic Duels is a free to play game. Though it requires a lot of time to unlock all cards and bd able to compete with other players.