My personal recommendation to everyone, all the time, is to have at least 1-2 characters each on both servers. (Unless, of course, you are someone who is absolutely hardcore insistent on having one and only one character with no alts, ever.)

I didn't even realize I could have alts on both until I'd been playing for about a year after I started playing, and I wish I'd done it from the beginning. (Luckily daily rewards had not started yet at that point.) Look, the EU server is the one that has the most issues, but in my experience, there have also been a handful of times when the NA server is the only one that's down. Or sometimes, rarely, I want to do group content, and it's an off-time for one server or the other. It's always good to have options, and if you create and do some early leveling of those alts now, when you aren't specifically having problems yet, they will be sitting there waiting for you if (when) you do have problems with the other server.

It's much less frustrating when you can say, "oh well, can't log in just now, I'll just flip to the other server and play another character I enjoy!"

Edited to add: I can't advise you on the technical ramifications. Everyone's experience seems to vary so wildly. I will just reiterate, it's worth a try, and the more options you have, the better.

I live in London, UK, and have my primary account on PC-NA. My ping is generally 160-190 ms, with occasional spikes to 215 ms or so. I find this entirely playable.

In contrast, my ping to PC-EU is 60-90 ms, but I have many episodes where my button presses simply don't get through to the game despite this apparently low ping. I intensely dislike dying because neither block nor roll-dodge nor heal have made it through.

on PC it may be different, but on xbox my experience is:

On NA, people have a more agressive attitude in public. I often get attacked (without consequence) in public, summerset chat often insults in contrast to EU (on EU you have it in Auridon though).

Nevertheless also friendly players, joining a guild might be even more recommended than on EU to meet people to have fun with.
I don't think that people on NA are less polite, there simply are MORE people so there is also more bad behaviour.

Trade system is pretty different. On EU, you pay no dues to use a guildshop, on NA it is required in the major trading locations. This has influence on prices, cheap ingredients are more expensive, on the other hand gold mats are slightly cheaper.

I have more sales (focus on food/drinks/furniture) on EU than on NA.

Concerning lag I see no big difference, but I play no vet content. Daily delves and worldbosses. Loading screens slightly longer on NA but as I use an external SSD acceptable.
The worldbosses are MUCH easier on NA, as there are many more players around.

I skip Summerset worldbosses on EU completely meanwhile, as I had to solo them, on NA I can do 7 quickly each day as I never have to wait very long for other players to join.
In Elsweyr I skip Kee'va on EU, too difficult to solo for me, on NA quickly done with others.

As a sideeffect, people on EU often use cheer and celebration emotes after defeating a worldboss, on NA they just ride away. But the lack of players on EU also leads sometimes to form spontaneous worldboss hunting teams, where they share their quests and finish them together. With less players, teamplay becomes more important.

So in general, it depends a bit on your preferences.
I would recommend, to try both, before you start to invest crowns in addons like outfits/mounts etc., as you had to buy them twice for both servers. So try and find out which one you prefer, focus on that one, and keep the other as backup in case of problems (lag, login problems).

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I forgot: on EU, Cyrodiil non-faction locked campaigns are deserted, on NA enough people so that you can gain AP. I prefer it to the faction locked campaign, as keeps are more frequently lost and won, so quicker AP gain.