Joye brand 510 - the slim ones have short battery life and I strongly strongly recommend manual batteries which make it easier to get a good hit and the 510 ones are sealed and safe from being damaged or killed by juice leaks. Since they are sealed you can also use a drip tip on the atomizer. try Boge 3 ohm cartomizers for your favorite juices (I use PG juices with 20% or less VG and get good carto life).
The other most popular slim model is KR808D-1 (Vapor4Life is like the manufacturer model, and the other style is SmokelessImage Volt, Bloogplanet Maxxfusion, Halocigs G6) and again I recommend manual batteries. The Vapor4Life manuals have an easier to press button and the others are more completely sealed but have a harder to press button.
Cartomizers are disposable though some attempt to clean and dry them for inconsistent additional life. I can get 7-10 days use out of a carto w/ thin juice (PG w/ 20% or less VG)
mah - how long a battery lasts. 100mah is about 1 to 1.5 hours of moderate vaping. Slim ecigs typically 180mah for short ones and 280mah for long ones.
For the biggest hit and the longest battery life, you skip slim ecigs totally and look at models like Joye Ego and Riva 510 at Liberty-Flights.com (press the 2-% off fist - upper left front page). That one shop is known to have the 3.7v Riva 510 kits. Lots of places have Joye brand Ego. Many other places have clone Egos, some of which are not made well. These models have batteries 650mah+ and can optionally use the hotter low resistance (LR) atomizers and cartomizers. In additon to the fat battery models like these, there are a variety of mods of various shapes that use removable industrial batteries.