Other starter tips:
Start leveling your horse riding skill NOW. It costs 250 gold to raise speed, carrying capacity or stamina by one point, and you can only raise it one point per day. It takes 180 days to raise all to full. Speed makes the horse faster, capacity adds more inventory space to your character, and stamina just makes it harder to knock you off the horse. Any horse will do, there are just tons of skins but they don't affect the underlying settings. Each CHARACTER has different mount settings, but any one character has the same settings on every mount they have. You can have 10 mounts for a character and they all have the same speed, capacity and stamina.
If you want to craft armor, weapons, food and potions, start that up right away too. The armor and weapons can take a long time to get all the traits researched.
Join the fighter's guild and mage's guild in the game. You don't have to actually do their quest lines, just join them. Killing daedra and undead raises Fighter's Guild level and finding lore books raises Mage's Guild level. There are some valuable skill lines under each.
If you are on PC (sorry console players), google "ESO Minion". There are game add-ons for PC that make life much easier, such as maps showing where all skyshards and treasure map locations are, better game UI, etc.
Every three skyshards found give you a skill point. This becomes very important as you learn a ton of skills and develop passives for class, race, etc.
You get XP just for discovering new locations, and finding wayshrines makes jumping around between areas much easier, so explore!
At first, you want to have some of each armor type (light, medium, heavy), as just wearing it in combat raises your level with the armor and unlocks passives you can spend skill points on. You have plenty of time before you hit level 50 and accumulate 160 Champion Points to get everything maxed out.
On new characters, I tend to have 3 or 4 skills I use a lot and at least one that is on the bar just to raise its level, Until you are maxed out, you will always want to have a skill or two on the bar that are there to level it up instead of having 5 maxed out skills and a lot of undeveloped ones.
If that first mount is too expensive in gold, I might be able to give you the gold for it, or you can even use the Crown Store (real money) to buy a mount skin you really like. As I said earlier, all mount skins have the same stats for a character, so you can raise the stats on an ugly one, get a shiny one later, and it will have the same stats. If you bought the Imperial Edition of the game, you can buy the Imperial horse for 1 gold.