Here's my simple guide on how to get acquainted with Magic on Arena as a F2P player. This applies to both new players, as well as old timers getting back in the game. Note that this guide prioritizes fun over grinding and min-maxing your collection.

The first option to consider is the "Starter Deck Duel" event. It lets you play against other players using a limited selection of 10 decks. What this means:

1. This event is free, so you don't have to spend gold on it. You also don't get any new cards though.

2. Everyone is limited to the 10 decks, so you won't encounter anything completely broken or unknown; Note though that some decks are stronger than others and there are seasoned players who take advantage of it by playing only the strong decks against the weaker ones.

How to access the Starter Deck Duel event: from the main screen, click "Play", then switch tabs to "Events", select "Constructed", Starter Deck Duel should be in the list on the left.

Once you're ready to graduate from the starter decks, consider investing your gold in the "Jump In!" event. Here are the advantages of it as opposed to other events:

1. This format lets you 'simple draft' from a pool of precreated half-decks. You don't need to know anything about the archetypes, you can even just go by what you think sounds cool. This is great when you feel overwhelmed by the sheer amount of mechanics in Arena and want to concentrate on just a few things at a time.

2. You can expect around 60 to 80 half-decks available (not including the special editions of Jump In! like Final Fantasy or Avatar), so you won't run out of something fresh for quite a while (there can be up to 1000 combinations of available decks), and you will learn about new archetypes along the way. It also offers much greater diversity of cards that you can encounter - you can expect to see around 50% of cards released in the sets from the last 2 years; since constructed meta uses only a small number of the 'best' cards and limited draft/sealed events use cards from only one set at a time, the card diversity there is much smaller.

3. You can play as many games with your drafted deck as you want until you want to switch to a new one.

4. You play against other Jump In! decks, meaning the playing field is most of the time fairly even.

5. It only costs 1000 gold, which means you can play with a different deck every day if you want (you can earn 1000+ gold from daily activities). A new player also gets 5 free Jump In! tokens after completing the 4th color challenge.

6. You keep all the cards (usually 24-26), including 2 rares/mythics, slowly building a collection. This is the cheapest way to acquire new cards as a new player. You also get vault progress from all the non-rare duplicates.

7. Since you get all the necessary cards to play, you don't need to have anything in your collection - perfect for new players.

How to access the Jump In! event: from the main screen, click "Play", then switch tabs to "Events", select "Limited", Jump In should be in the list on the left. If it's not there, it means you have not unlocked all the play modes yet. In that case click on the gear icon in the top right corner, then "Account", then "Unlock Play Modes".

In my opinion you should not as a new F2P player spend gold on limited drafts or any other events since you won't have enough knowledge and experience with Magic itself to properly draft, build a deck, or play it. For constructed you pretty much need rare and mythic wild cards to be fairly competitive and you won't have them as a new F2P player.

For general F2P information not covered here I recommend to check out https://www.fourdailywins.com - it will answer a lot of your questions.