What I did when I first started was play Arena when you have gold instead of buying backs. I did this for two reasons:
1: If you put time and effort into truly learning how to get good at arena you'll be able to win more often than not. If you win 4 games on average you'll find yourself roughly breaking even (your rewards will be worth about the 150 gold entree cost).
2: In the mean time, you just played ~7 games of hearthstone with new cards and an EVEN footing. That is fun to me. Losing to decks I was unable to craft was not fun, and knowing I couldn't hit legend if I tried was not fun.
3: Eventually if you put enough effort into arena you'll find yourself able to win 6+ times on average. (some times I'd win 9+ back to back, and sometimes I couldn't break 3 wins -- streaks happen here as well as anywhere, keep your chin up). If you win 7 games on average you will get your rewards also including 150+ gold. This means you basically get a free pack, which is awesome for new players. I think I averaged about 6 wins when I was "arena farming" packs, which was more than enough in combination with dailies to casually play arena as much as I wanted.
That being said, arena and ladder are quite different. Getting good at one will not make you good at the other. Ladder is very much about knowing how your deck interacts optimally with the decks currently being played, and knowing what deck to play when. Arena is very much about playing whatever card is strongest vs two others while trying to fill a curve and a general overarching strategy (tempo vs late game value).
This is starting to ramble, so I'll wrap up.
*I found arena more rewarding as a new player because my card pool wasn't holding me back -- my newness was (and that is okay). Playing casually you can pretty much do as much arena as you want (assuming 4-5 arena runs a week while completing dailies), once you get the hang of it (5+ wins avg). If you want to play all day every day, you're going to need 7 wins a round.
*Find a pro's arena chart and follow it to the T. It will give you the best pick 90% of the time. Jump ship if you absolutely have to fill out your curve. Look up a guide on tempo/aggro and control/value arena curves (it's pretty simple).
*To get "better as a player" focus on card value. It's easy to clear the board and spam creatures every game by turn 3-4 -- but you'll find yourself with an empty hand and 1-2 weak creatures on the board.
*Regarding when to surrender -- When you know your deck doesn't have threats left, or has no way to come back. When they have a stronger board than you know you can place, and they have 4+ more cards in hand -- you can probably give up. That being said come backs are pretty reasonable to have happen and very rewarding when they do. They're also pretty much the only way certain match ups can win (Pretty much anyone vs face hunter).
If you have any questions or just want some more advice, feel free to PM me your battle.net tag. I'm a pretty casual player, but I have most the cards from starting back in beta and probably playing half of the months. I still can't netdeck the full control warriors, but I have most of the meta legendaries. Skill level I'm again pretty casual, but I've peaked 2-3 games off legendary despite playing very casually (Let's be honest, the 150+ games it takes to hit legendary can feel ridiculous). I used to be solid at arena too, but no longer actively play it.