Playing ESO in a first person offers a very exciting, focused and immersive experience you'll hardly find in other MMOs. However, it comes at the cost of reduced visibility and awareness. But, in my opinion, with some basic tricks and a little training this cost can be greatly mitigated and thus make the experience much more pleasant.
#1: Don't gimp your character: Some people just accept that by having a reduced view they are going to take more hits in combat and so to correct this they dump lots of points into health, making their character more sturdy but also less effective. First person players are very hated because of this. Don't turn yourself into a noob, learn to avoid damage like everyone does and if you are a DPS class keep your DPS high.
#2: Set your first person field of view to 130. You can find this option in Settings -> Camera. You'll get a wider vision which is always good and it won't hurt your immersion at all.
#3: Keep an eye on your UI. There will be things happening that you won't see on the screen but you are still perfectly able to notice them. Constantly check your group's health bars and your own.
#4: Set your active combat tips to "Always Show". You can find this option in Settings -> Interface. This option has a tutorial purpose, but we use it to increase our awareness. If you are inside an AOE you'll see a message telling you to double tap in order to dodge, if you are being targeted with a heavy attack you'll be told to hold your right click in order to block... You must pay attention to these pop ups because they will let you know when you are about to be hit with something and act accordingly, even if you can't see it.
#5: Use the "Combat Indicator" Add-On. It's a very simple utility that will turn your compass red when you are under attack. If you can't see your enemy he is probably beside or flanking you.
#6: Keep yourself moving, specially if you are playing melee. By this I don't mean to jump around like a madman; keep hitting your target but at the same time cover all the angles with your vision and gather all the possible information from the battleground. Know how many enemies and what type they are even if you can't directly see them.
#7: Not a real tip, but if you want to ride in first person mode there is a cool Add-On for that too called "Immersive Horse Riding".
I know many of these lines are generic information. Still, there are many little things I mention here that I wish I had known earlier. I hope this helps somebody enjoying the wonderful world of Tamriel in all its beauty... And feel free to add any suggestion you might have