Back when we only had atomizers (used with cartridges or used only for dripping) it made sense to clean them because of their cost. I used denture cleaner along with the inexpensive sonic cleaners for dentures which worked OK. The best thing was a steam cleaner, the kind that sort of looks like a teapot. I would hold the atty with a pair of tongs and give 3 quick bursts of steam into both ends. Drying them with several bursts of canned air sped up the drying process. If the wick wasn't dry, the atty wouldn't work very well and I needed to let it air dry for a day or so. Also, when this was done, I had to be prepared that I might kill the atty.
Then when cartomizers became available, they were wonderful. I tried cleaning cartomizers a couple times. It wasn't worth it. That was 5 years ago. Then I saw a video of PBusardo boiling them. I think he boiled and rinsed 3 times, until the water in the pan didn't have any foam floating on top. I think there was some blowing through the carto involved as well. I remember doing that. It was not fun. I never went through all those boilings; too much work and time involved. I don't think a cartomizer ever got back its "just like new" self after cleaning anyway.
If we are just boiling attys, then that kind of makes sense. Doing a careful dry burn is probably the most effective way to clean the coils. The denture cleaner is kinda fun because it's fizzy and could probably loosen some of the gunk before doing a dry burn. Also the tablets are good to keep on hand for cleaning all kinds of stuff. If you're going to get some, there are little battery-operated sonic cleaners in the store next to them. They can give a little more cleaning power and also are good to clean jewelry.
Some good cleaning utensils are disposable mascara brushes (I got a pack at Sally Beauty Supply). They are very inexpensive. While you are at Sally's, take a look at all the acrylic nail decorations. They are fun to use to decorate your e-cig. You can really bling it out if you want. Also, for cleaning even smaller crevices, the little picks used for cleaning between teeth, braces and bridge work are good too. They come in 3 sizes. (They are in stores that sell teeth cleaning stuff, not at Sally's.) Disposable mascara wands and the dental pics are like tiny bottle brushes and I've used them to clean other things as well.
Now that I found a clearo-tank I like, I want to decorate it. I have two e-liquid flavors I like and two of the tanks. (In hindsight, I should have ordered them in different colors.) I like the little drip tip that came with them so now I really need to mark the tanks in some way so I don't get them mixed up. My big collection of acrylic drip tips are a fun kind of jewelry, but after using them for a while, their little O rings get smashed down and the fit isn't tight. So I've just been using pliers to squeeze the carto edge until it is a little bit oval shaped and fits tight around the drip tip again. I have some O rings to replace the ones on drip tips, but so far haven't tried them. Just getting the old O ring off of a drip tip will need some kind of tool, a pick or pin of some kind. Maybe I will try that if I can find the O rings I got so long ago. (I can't squeeze the tank cap, lol.)