Hmm, this is a pretty broad topic that doesn't necessarily have a super simple answer but there are a few easy ways to get started:
You might want to start with a "replaceable head/coil" atomizer first. something like one of these:
Vision 5ml Nova Tank Clearomizer, V2
Vision 2.0 Clearomizer
Those have a tank and when the coil is dead you can just replace the coil head for pretty cheap. If you are looking for something simple int terms the ease of replacing a coil then this is the best place to start IMO. That being said this might not be considered by all as a true "rebuildable" as you are still using some premade coil at a set resistance. The good news is that you can, with some patience, actually rebuild the coil and wick in the head on your own to improve/customize performance. This brings us to a true rebuildable.
Now, a true rebuildable would be considered an atomizer that you would build the wick and coil yerself, meaning an atomizer that doesn't really have a modular replaceable coil head, just mounting points for your own coil and wick. The advantages to this type are many but the learning curve is also a bit more involved but I think many can agree that it is well worth it.
Rebuildables can be categorized in 2 forms, a rebuildable (dripping atomizer) or a rebuildable tank atomizer. The reason I mention a rebuildable dripping atomizer is that is is typically easier to start out rebuilding on one of these and learning the basic techniques of coil-making and wicking before stepping up to a the better rebuildable tank atomizer as they usually are more advanced in terms of wick and coil styles.
good place to start for a true rebuildable:
Phoenix Rebuildable Atomizer - Clone
It's cheap, it's pretty easy and actually works really well
The list of rebuildable tank atomizers is very very long as there are many different types with many different price ranges.
This one is a good cheap start:
The Griffin - Rebuildable Atomizer Tank
It is pretty new to the market and is basically a cheaper copy of one of the better and more popular rebuildables out there (The DID). It has almost all of the performance of many of the higher end atomizers but won't break the bank.
As far as wicking materials go, that is a whole other talk show. Silica has been used is atomizers since the beginning but some have concerns with it being unsafe. Cotton has become very popular as it tastes awesome, wicks extremely well but does have it issues regarding preparation. Stainless Steel mesh is extremely popular as it is used in the majority of the better rebuildable tank atomizers but probably has the biggest learning curve for getting it just right.
With any of the rebuildables it might seem kinda daunting and complicated but with a lil initial patience, practice and learning they become extremely simple and you will end up spending mere pennies to replace a wick and coil compared to cartomizers or atomizers and they work way better too
