There is so much choice in this game and so much to learn so here are the tips I wish I knew when I started that really help you get the most xp out of playing early on:
1: With your first skill point equip a weapon and a weapon skill straight away (super obvious but super important).
2: With your next 3 skill points equip one skill from every class line (start getting xp for all class skill lines straight away, you might think one or two aren't that good but trust us all the passives are great at high levels and you want to get that xp up as quick as you can so you have more choice and freedom later on).
3: Equip Soul Trap (world skill). You are given this skill for free upon completing the tutorial dungeon for a reason: If you don't have it and you need it you will cry. Buy level appropriate empty soul gems from the mages guild asap: you use trapped souls to revive yourself (and others) when you die and also to recharge weapons. Soul Trap is also a handy ranged damage spell early on, though later on it become purely a utility and so you'll never need to morph it.
4: Equip at least one piece of each armour type (start getting xp for all of them straight away, for eventually the passives at high levels are all fantastic). You will probably choose the type you want to master later on but for the first 20 or so levels its great to get all the bonus xp while you decide. Most people decide to go with a five of one type + two of another mix of armour eventually as it gives the best combination of passive rewards.
5: Increase your inventory size (it only costs 400 gold the first time). Find a pack merchant and just do it (there is one in almost every town).
6: Get a Boon (from a mundus stone). Get the first one you find (because you can) and then once you find more choose the one you need (you can only have one active at a time).
7: Don't morph skills straight away. It's tempting I know but your skill lines only get xp if skills from that line are on your skill bar so having two umorphed skills from the same line equipped will level that skill line up much quicker than having just one morphed skill. Holding off the urge to morph and customise you skill load-out early on will be rewarded by far more xp to all your skill lines and will allow you to keep some skill points around to fill up you skill bar asap and for all those great passive skills (and if later on you decide you don't like an active or want to try out a new one you wont have wasted skill points in the old skill by morphing).
8: Get a heal. There is no trinity in this game, ever character has a self heal or life steal skill (or at least can learn to make themselves awesome potions). This is so important when you are solo-levelling (and also really helpful if you're playing in a group - you'll make the healer far more effective on the whole group if you can heal yourself some of the time). The amount of death you will avoid by having even the smallest way to restore some health is undeniable.
9: Get Intimidate and Persuade. The first passive skill in both the fighters guild and mages guild skill lines give you the option to intimidate and persuade NPCs which greatly improves quest efficiency (by allowing you to skip stages of a quest or receive extra bonuses/rewards from NPCs). Even if you never use a mages or fighters guild skill take both these passives early on (after you have filled you skill bar with actives first) to greatly improve your questing efficiency, both skills are available the second you join the respective guilds (you can join both guilds right away).
10: Deconstruct everything! Money is mostly obtained from quests and is more than enough to repair/buy materials while you level. The xp and resources you get from deconstructing are invaluable and help you level up a craft skill (or three) from the second you start adventuring. You'll probably only realistically max out two crafting skills skill points wise but that doesn't mean you cant max out all your skills through deconstruction (though watch out for the deluge of crafting items if you choose multiple skills at once, bye-bye inventory/bank space). Deconstructing items not only give you all the resources you need to craft (you will never need to farm again) it also gives three times the xp of making the same item. So dont craft to level, deconstruct to level. This game is geared towards a player being able to make the best items in the game for themselves so get a foot in the door and start deconstructing early and then choose what you want to make yourself and never buy an item at a shop again (you'll save a mint sticking to home-made items and loot). Alchemy and provisioning do not support deconstruction.
Bonus Tip 1: Get all the skyshards straight away whenever you enter a new zone (the above ground ones are easy to get without a fight and getting them when you first enter a zone ensures you have the lay of the land and will have discovered many various wayshrines by the time you start questing. Once you have the right level/gear/group you can sweep up all the underground ones before you leave the zone.)
Bonus Tip 2: : The fastest way to level up a skill line: have multiple skills from it equipped and then hand in quests, completing quests gives you the absolute most experience (quest xp translates into skill xp for all you skills and then a boost from every active on your bar to its own skill line.). Once you hit level 15 and get a second bar you then have the option of having your "main bar" (which you use in combat) and a "levelling bar" (which you switch to quickly before you talk to anyone to unload all that conversation and quest experience into the skills and skill lines you are trying to level up.
Bonus Tip 3: If you find you are always running out of inventory space make another chanter. All you character share a bank and so you can withdraw a ton and dump it on your new guy making plenty of space for your main (you can skip the tutorial cave on all your new charters and start off right in town). You can have up to 5 character per account per server and making a new one can be much cheaper than spending gold to upgrade you inventor/bank.
PS: Don't spend money on travel. Ever. Walk to the nearest wayshrine and you can use it to travel anywhere on the map that you have discovered for free. So much money to be wasted by impatience. Take the time and save your money for repair costs. You will thank me.