The three most popular minis are 510, 901 and KR808D-1 (aka Vapor King at Vapor4Life).
510 - cart unit with many options, maybe less flavor with carts but bigger hotter hit?, cartos available
901 - good flavor and easy drag but a softer airier hit, don't know if cartos available
KR808D-1 - dedicated cartomizer unit (but you can also put a 901 atty and carts on it w/ no adapter, or 510 w/ adapter)
All available w/ manual
batteries
Each of those also has a fat battery long charge life version available - Ego or Riva 510 (based on 510), Riva 901 (based on 901), Elegant Easy (based on KR808D-1). \
Of the three, I would say the 510 in general and its fat battery models have the most options available - the most kinds of carts and cartomizers and atomizers etc. And if you get a 510 I recommend Joye brand because there are some substandard clones around - some people getting kits with parts that don't fit etc.
buy Joye and you should get a good one.
If you want more of an intro, in the sticky threads at the top of New Members see
1. the Newbie videos
2. the thread with Library in its title (leads to an illustrated multipart guide)