So, besides armor and weaponry, what other stuff you give to your follower? Like potions for instant. Is it necessary to give them potions? Do they use it? And what other things you give to followers that are useful to them?

Torch, Tankard, Food and Drink, Books, jewels and scrolls.

Followers can use health potions but not sure if they can use others.

I give my followers enchanted amulets, rings and armor enchanted with fortify (health, heavy/light armor, magicka, stamina), resist (fire, frost, shock, magic) and muffle, if appropriate for sneaking characters.

I give my followers nothing special. A set of armor I may come across and perhaps an enchanted staff if I want to watch them spit spells.

Usually a decent set of armour that they can wear together with a good weapon or two and all the heavy valuable loot I don't wish to carry.

Healing potions, and they use them. Proper weapons, scrolls, jewellery and staves, armour, accordingly to their speciality. Money when I dismiss them and I don't take back the stuff I gave them.

Depends, on what I want them to use. Generally better armor, better weapons, potions, food and of course some heavy stuff, but I generally RP that my followers are friends/companions not just paid followers. One of my non-magic using characters gave Marcurio every magic item they came across, including The Sanguine Rose, they being fellow mercenaries, that was their deal. ( Didn't take anything back from him but the books he helped to carry.)

What if you give them spell books. Are they capable of using the spells or not?

No.

My standard practice is to provide my followers with tempered weapons, along with enchanted (and tempered, where applicable) armor & apparel. The enchants are magic resistance, muffle & either health/stamina or health/magicka, depending on the follower's class. In some cases, I'll also throw health/magicka/stamina regen in the mix.

I give my followers

...Good armor/robes that matches their combat style and is smithed as high as possible and enchanted, mainly with Fortify Health, Fortify Magicka (for mages), and Muffle for the boots.

...Good weapons matching the combat style, smithed as high as possible. Mages might get a staff, but nowadays I avoid giving any followers AOE staves, especially fire balls. They usually get a simple dagger to wear when "off duty".

...Healing potions (bought, not crafted, since most don't seems to use the crafted ones)

...Magicka potions and Elsweyr Fondue to mage followers. Only one or two at the time, though, since they (especially Marcurio) have a tendency to use them as soon as they enter combat, even if it's just some wolves.

...A set of ordinary clothes to wear at home or at inns.

...A fur cloak and hood when we're in colder regions.

...Some food and drink, for RP purposes

...A torch or lantern

...Some get some other items as well, for RP purposes, mostly books. Marcurio carries books on Dwemer or Ancient Nord history, since that seems to interest him. Serana, who has been locked away from the world for so long, is carrying a few history books (like "A Brief History of the Empire").

the Best looking weapons and armor that fit their style, and also the junk i am unwilling to carry.

You mean my pack mules? I'll give them an apple or carrot after a long haul and pat their neck when they've done well

I'm gradually upgrading their armor. Steel-Plate for Faendal and Ebony for Lydia are two examples.

The only unique item I gave to a follower was Lydia. It was the Drainblood Battleaxe which she has strapped to her back.

I use the Realistic Lighting Overhaul mod. It's dark in Breezehome Sir.

Lydia is my portable chirping mini-magelite for the age of Yore.

Mrs Dragonborn can now find her pants first thing in the morning.

"Grey clouds are gonna clear-up, put on a yappy faice..."

Upgrade armor and weapons as I can. Enchanted jewelry that suits them and some healing potions.

Question. If Jenassa has a blade enchanted with soul trap, will she fill soul gems? I've never tried it before as I always filled enough on my own. I happen to be playing a character that isn't usually in position to fill them and she is.

They do use them.

I give them potions as well as food, some misc items and stuff. Also, when we do some dungeon-crawling I always split rewards with them, and if they aren't friends but hired mercs I give them set amount of gold every week. They also carry their own tents and other camping gear.