First of all, You should know that Hearthstone is based on both skill and luck, sadly you can't control the luck part (unless you know some voodoo witch), but you can try to improve your skill level, hopefully this guide will help you improve at playing Arena by getting you to pick the best class possible at any draft.
What class should you pick ? :
There are many things that goes into count in having good Arena scores, and one of the most important parts is picking a good class, and while you can have 12 wins with any class, it's all about consistency, especially if you want to keep your gold stash high.
What is Arena all about? :
First of all, you should never compare Arena with Constructed, therefor you should not make a picking decision on how the class does in Constructed because it has little significance to Arena.
In Arena you can't really chose what type of deck you're gonna have, sometimes you get to have a very aggressive deck and some other times you get to have a slow control deck, but most of the time you will have a random deck that's good on both fronts but doesn't excel at any of the two.
And this information is helpful because usually these types of random decks are tempo deck or control decks, and therefor you should pick classes that are good at those roles.
Also when picking a class you should think about two factors:
1- Hero Power :
In Arena you can't control the cards you pick that much, and sometimes how ever much you try to get a good curve, you find yourself more often than not with a bad hand, to remedy this, Hero Power comes to play, as we talked earlier, Arena decks are usually random tempo and control decks, so you should pick Hero Powers accordingly.
2- Common Class Cards :
In the drafting phase of Arena, you get to chose a card from a set of 3 cards of the same rarity, and obviously you have more chances of getting a set of basic or common cards than getting a set of rare, epic or legendary cards.
Therefor you should try to aim for classes that have good common and basic class cards.
My personal Arena Class ranking :
9- Warrior (3/10) :
Hero Power (1/5) : Health is not as important in Arena as controlling the board, and Armor has little to no play in doing so.
Common Class Cards (2/5) : While Warriors have some of the best class cards ever which are Weapons (Fiery War Axe, Death's Bite), but they are so few in comparison to the other cards, so more often than not you when picking Warrior you will get to pick from bad or very situational class cards.
8- Hunter (4.5/10) :
Hero Power (1.5/5) : The only reason I'm giving this a 0.5 more rating than the Warrior Hero Power is because in some cases you get to pick an aggressive deck and so you can benefit from your Hero Power at rushing your opponents down.
Common Class Cards (3/5) : Hunters have all around average common class cards. Sometimes you can get the occasional good "Animal Companion" or on of the weapons, but even if you don't, you will get to chose from cards that aren't actually all that bad.
7- Warlock (5.5/10) :
Hero Power (3/5) : Health is not as important in Arena as controlling the board, and Armor has little to no play in doing so.
Common Class Cards (2.5/5) : Warlock common class cards are a swing and miss, they are either very good like "Soulfire", "Flame Imp", "Dread Infernal" or really really bad like "Sacrificial Pact" or "Corruption".
6- Shaman (6/10) :
Hero Power (3/5) : Totems sometimes prove to be really helpful to give you some kind of board presence when you're out of cards, and the utility some of the totems may prove helpful in some cases.
Common Class Cards (3/5) : Almost the same problem that Warriors have, Shamans have some really awesome common class cards like "Stormforged Axe" and "Fire Elemental", but unfortunately the other cards are just plain bad or too situational and more destined for Constructed .
5- Druid (7/10) :
Hero Power (4/5) : Druids' Hero Power is solid, it helps at controlling the board, and while it's not as good as the Rogues' Hero Power that have 2 charges, it compensates a little of that with the armor it gives you that helps with not overextending with the trades.
Common Class Cards (3/5) : Druids have a great set of common class cards like "Swipe", "Druid of the Claw" and "Iron Bark Protector" but they do also have some average to below average cards that are not fit for Arena like "Savage Roar" and ".
4- Rogue (7.5/10) :
Hero Power (4.5/5) : Rogues' Hero Power is awesome, and is great for Arena, it helps a lot at controlling the board, and it can be combo'd with some common class cards. The only down side to it is maybe overdoing it and using too much health in the process or the ability to not go over taunt.
Common Class Cards (3/5) : Rogue common class cards are somewhat average, with the exception of Weapon enchantments who are above average, or the bellow average spells like "Shadowstep" and "Sinister Strike".
3- Priest (8/10) :
Hero Power (3.5/5) : You might think that this is like the Warriors Hero Power, but you're so wrong, while it can still serve the same purpose as getting 2 Armor, but it can also be used to heal your minions, which can be very helpful when doing beneficial trades.
Common Class Cards (4.5/5) : Priests have a great set of common cards, and the great thing about them is that they fit so well in Arena, either by being a great minion card like "Dark Cultist" and "Temple Enforcer" or by being a great spell like "Power Word: Shield" and "Velen's Chosen".
2- Paladin (8.5/10) :
Hero Power (4/5) : Most of the time Arena is all about board control and winning in Value, and Paladins' Hero Power is just great at doing that. The 1/1s are very helpful at giving you card advantage, and if your opponent can't handle them quickly they can get out of control.
Common Class Cards (4.5/5) : Paladins have one of the best 2 drops in the game "Shielded Minibot" and one of the greatest weapons in the game "Truesilver Champion", and the other cards that they have are above average like "Concecration" and "Blessing of Kings" which are very good in Arena.
1- Mage (9.5/10) :
Hero Power (5/5) : Mages' Hero Power is better than both the Druids and Rogues' Hero Powers because of the ability to avoid damage and going over taunt, so it's a great tool in Arena.
Common Class Cards (4.5/5) : Solid spells like "Frostbolt" and "Fireball" with the ability of going face and surprising your opponent with a fast kill not to mention the awesome "Flamestrike" which is one of the most toxic spells to play against in Arena, and the other cards are average to above average including some of the secrets.
I hope this post was helpful to you, please don't forget to post your feedback which would be much appreciated. Thank You.