These are popular choices since the most supported threadings are 510 for 2-pieces and KR808D-1 for 2-pieces
re battery life
180mah is at most 2-3 hours for a light to moderate vaper. 1/2 that for a heavy vaper
180mah is 60% more charge
750mah is a LOT more charge
3-piece is battery+atomizer+cartridge aka cart
2-piece is battery+cartomizer aka carto
And manual batteries recommended for all - you can control your hit better, much harder to kill with juice leaks, and won't turn on accidentally from wind or vibration. Cartomizers and dripping are the most popular methods of
vaping and those are the ways most likely to drip on a battery occasionally.
Joye 510 - 3-piece usable as a 2-piece with mostly blank cartos, 180mah, small (especially w/ a carto) - very nice PCC available at NoSmokeVA.com for standard 510 batteries (manuals included) but tI think if you open the lid you need to restart the charge
Joye 510 w/ mega xl batteries - 280mah but long (128mm w/ a carto, longer with atty and cart), only the less-roomy Joye metal PCC available
KR808D-1 (also Vapor4Life.com in colors, most prefilled cartos there) - a 2-piece with lots of prefilled cartos and good selection of blank cartos. Batteries - shorty 180mah, standard 280mah, xl380mah but xl won't fit in the PCC which is a flat metal case. Can be used as a 3-piece w/ a DSE901 atomizer
The fat battery models - these have super-long battery life of 650mah to over 1000mah depending on what batteries you get
Fat battery models can also use hotter-hitting low resistance atomizers and cartomizers
These two are 510 compatible
Ego - the original fat battery 510
Riva 510 - a popular less expensive clone (I got the Riva 510 Lite Bundle for under $30 at Liberty-Flights.com - click the 20% off in the upper left corner of the front page then all prices shown will be shown reduced by 20%)
And this one is KR808D-1 compatible - Elegant Easy from CigEasy
In order of heat of hit:
510 ... KR808D-1 w/ Vapor4Life cartos ... Ego/Riva/EE w/ LR atomizer or LR cartomizer
Some good hardware vendors
Liberty-Flights.com (click the 20% off on front page upper left - I need internet Explorer to see it)
Cignot.com
LiteCigUSA.net (has plain KR808D-1 manual kit)
NoSmokeVA.com - for the nice PCC for standard 510
And you need
eliquid - no matter what you get you need to add e-liquid