Daggerfall isn't Skyrim. You can't expect to be able to experience everything in one character - if you work in the Fighters Guild and the Mages Guild, you will end up doing quests that conflict with the interests of the Necromancers, Dark Brotherhood, and Thieves Guild, and they won't like you for it. So if you want to experience
everything the game has to offer, expect to do multiple play-throughs.
Some other tips for you:
When you first start playing the game, DO NOT TURN OFF THE TUTORIAL. It contains VERY MANY useful tips that will help you get a bearing on the world of Daggerfall.
Once you're out of the initial cave and in Daggerfall city, the first thing you should do is look for work. The Very Important People will begin contacting you on their own as soon as you start making a name for yourself among the common folk.
Most people don't have anything important to tell you. The townies are really only good for asking directions to places. Don't try small talk with them - you'll just confuse them (and yourself, probably!). You should also usually leave the "Blunt" and "Polite" buttons in the dialog window alone, since it's pretty much impossible (and pointless) to tell if the people you're talking to prefer one way of speaking over another.
As Benefactor said, the quests in this game are timed. You'll always be given copious amounts of time to complete a quest, but if you travel a lot and put it off then you could end up screwing up whatever questline you're trying to work through, so watch out. When I first started playing the game I wasn't able to complete one of the quests for the main questline in time and now I can't finish the main quest.
Healing potions and such are sold primarily by the mages guild and the various temple orders, but they won't even let you buy them until you've advanced within their ranks to a considerable degree, so make sure to research them all on the UESP and pick one that matches your character's abilities best.
Keep multiple saves of each character and SAVE VERY OFTEN! I like to save before I take on a quest, before I travel, before I enter a dungeon, before I buy/sell anything significant, and multiple times while crawling through a dungeon.
If you find ANYTHING Daedric, keep it and save your game. They're worth much, much more than they're weight in gold.
Speaking of which, gold will weigh your character down in Daggerfall - you can't expect to carry all of your vast wealth on your character at all times. So once you begin amassing a load of treasure, begin depositing it in the banks. In fact, as long as you're traveling your character should never carry more than a hundred gold coins on him at once. When you decide to go shopping or make large scale purchases, just take out a letter of credit - the shop keepers can then take/give credit from/to you as needed. The only times you ever need gold coins are when you buy food or a bed at a tavern or if you go travelling - in those cases, your business partner will only take hard cash. Finally, be aware though that each kingdom will keep a separate bank account for your character, so you'll have to keep track of where you've been storing all of your money as you play the game.
As soon as you can, buy a horse and cart and start saving up for a ship. The former will allow you to travel quickly and freely across the land the land of Daggerfall as well as provide plenty of room to store unnecessary items, and the latter will allow you to travel across the Illiac Bay without paying the exorbitant fees that the ship captains will charge you for travel.
Spells are very useful. If you're going to depend primarily on physical weapons, I'd recommend that you major in at least one school of magic like Alteration so you can use Resist Element, Levitation, and Water Breathing spells. Mysticism is also a useful school of magic that you might want to look into.
There are generally three ways to open a locked door: pick the lock (which is impossible if your Lockpicking skill isn't considerably high), cast an Open spell (which is sometimes the only viable method), or just hit it with your weapon until it busts open.
Some enemies are resistant to weapons of weaker materials. Harpies, for example, cannot be harmed by anything weaker than Dwarven weapons, which are pretty rare early on in the game, so be careful.
Minor skills are not dependable in almost every case.
Be careful when limiting yourself to certain armor types and such when creating your character - when I created my Argonian Nightblade, I gave her a disadvantage that prevented me from ever equipping her with plate armor of any kind, whether it be Iron, Steel, Mithril, Silver, Elven, Daedric, etc. It turned out ok since my character is very quick and agile and doesn't depend much on armor anyway, but the decision was still pretty reckless.
By the way, if you "use" clothing items in your inventory, then you can change their style. Tucked, untucked, w/ vest, w/o vest, buttoned, unbuttoned, etc.
If you don't have a levitation spell, you can scale walls by orienting yourself so that you're completely perpendicular to the surface of the wall, then walking straight into it. It will take a little practice to know when exactly you're looking straight at a wall (the compass helps with that sometimes) but if you keep walking into a wall like that in a second or two your character should begin automatically climbing the wall. (think about that - Daggerfall had players leaping across buildings at night, stalking people like hawks long before Assassin's Creed came along!)
Wow, I didn't mean to write a book for you or anything, but I guess that's what happened in the end.
I hope you find my tips useful.