I am looking to play as a Dunmer skilled with long blades and with a good moral alignment. Other than that, everything is up in the air. Which skills should I pick and which play style should I adopt?

Go medium armor, join House Redoran, maybe the Fighter's Guild, and wear bonemold armor. Definitely go with block too if you like one handed longswords as opposed to like a claymore. Also consider Marksman.

I particularly like using medium armor because it doesn't exist in subsequent games, and it really fits with a Dunmer warrior, and there are a lot of Dunmer-themed options for you - bonemold, Ordinator armor, etc.

Can you effectively specialize in both marksman and longsword? In other games I always pair marksman and sneak and become so proficient in those and so weak in my skill with blades that I abandon it entirely

You can. You just need to make sure that marksman is a major skill so you don't wast a ton of arrows at the beginning.

Just a note, House Redoran doesn't exactly pay well, so the Fighter's Guild really helps with trying to afford that bonemold.

A Dunmer character is a good "jack of all trades" type, so you can mix longswords, marksman, and some magical disciplines with no problem. Either Light or Medium armor are good; I'd even go so far as to suggest taking both as minor skills, and improving both, since they affect different attributes. The exact details of a build are only important for getting started in the beginning; eventually you can bring weak skills up through either practice or paid training. Morrowind is far more brutal on a starting character than the following games, but in the long run any character can do anything well (exceptionally well), if you're willing to work at it.

I had one Imperial character (the other "generalist" race) with a mix of Longsword, Marksman, and Sneak get too overpowered by Level 15 (hitting adversaries out to the limits of sight, and one-shotting even weaker Daedra with plain iron arrows from a minimally-enchanted Bonemold bow), so I ended up retiring the bow in favor of ranged spells just to keep it interesting. Trying the expansions at that level actually required bringing the bow out of retirement, just to survive.

No matter what you do, it is going to be painfully difficult in the beginning, but your character will improve steadily until they eventually become the most powerful thing on Vvardenfell. The satisfaction of noticably improving is one of its best features, and the rewards you get for trying things above your level are generally worth the risk. In the following games, you start out semi-powerful and more-or-less stay that way, unless you powergame or level inefficiently, and there are few good rewards because there are few real risks when everything is adjusted to your level.

Yeah, it is possible and probably encourage to at least join both. Though, I personally don't have much trouble with money it never hurts to have more.

House Redoran is something I need to very strongly recommend though. In Morrowind there are three 'Great Houses' that you can join which are themed Fighter, Stealth, and Magic just light the Fighters, Mage, and Thieves guilds, and as a Dunmer it really makes sense to join one of the Great Houses since, well, they're all Dunmer too. And House Redoran is the fighter-themed House. I find its quests to be pretty satisfying because you're often really trying to help people, like delivering a cure blight potion to a distant outpost to save a sick family. And the House is big into honor so there is a lot of trying to uphold and conduct yourself in the 'proper way' and in some cases actually restore or fight for the house's honor. Pretty cool, I think. And I don't recall there being much you have to do that is 'morally bad', which would be in contradiction to the Fighter's Guild which has a lot of corruption, though if I recall you can go down a path that ends with rooting out said corruption.

Yeah, morrowind (not the expansions though) can be finished with nearly any type of characters, because at lvl 25-35 you will be rocking any adversary even if your char build is far from "optional". What I always keep in mind regarding a new char is to get my endurance to 100 as quickly as possible, because when you level up you got 1/10 of your endurance to your health. So if you keep your endurance low for a long time, your health won't get high enough for Bloodmoon (difficulty=100 of course). And try to always get at least 3*3 attribute bonuses when level up. You can achieve this if you acquire training in those misc skills that's governing attribute is the one you want to develop before leveling up . Every 2 misc skill increases will give you an additional bonus point to your attribute when leveling, so for example if you train axe (governing attribute: strength) 10 times, you can be sure that when leveling up you'll get 5 bonus points to strength.