-Unofficial Skyrim Patch- is a must have, no questions asked. 1.9 official patch too.
-Skyrim Performance Plus- can increase your fps by range of 7-15, there's no reason NOT to have these. What they do is reducing resolution of rain, snowfall, leaves etc. These changes are not visible, unless you have Awakened Rinnengan that can see every individual pixel.
-Skyrim Project Optimization- from what I understand about this mod, it stops game from rendering things you cannot see. Results in fps boost, especially in interiors. Again, no reason not to have this.
-As mentioned above, SKSE and SkyUi. 90% of mods don't work without these.
-Unfortunately, a lot of good mods also require Official DLC's.
For installation conveniences, I'd say NexusModManager with LoadOrderOptimisationTool. But it's all on you.
That sums up what I'd call "must have". Now, instead of feeding your head with my fav mods, I recommend checking out youtube channel: Brodual
https://www.youtube.com/channel/UCMQkYC9HUcPTertReHILVOA - I hope no1 minds the link
These bros do short and informative reviews on mods. There are top 10 lists which you can look into.
Ofc, there are other channels that also cover mods, this is just only channel I actually subscribed to.
And finally, a tip. When searchin' for mods, NEVER ask yourself "Do I want this mod?". Instead, ask yourself "Can I play continue playing WITHOUT this mod?". If answer to the latter is NO, then download it. Hopefully, this'll keep you from flooding your load order with "immersive and what-not"-good-for-nothing-mods. Hopefully. It worked for me.