75W or higher, we recommend the Sony VTC4 2100 mah 30 amp CDR.
40W-75W = LG 18650HG2 3000mah 20Amp CDR
Samsung 18650-25R 2500 mah 20 amp CDR (green wrap if you can, blue wrap is just fine)
LG 18650HE2 2500 mah 20 Amp CDR
Sony 18650VTC5 2600mAh 30Amp CDR (* tested as only a 20 amp CDR)
AW 18650 3000 mah 20 amp CDR
Under 40W = LG 18650HG2 3000mah 20Amp CDR
Samsung INR18650-30Q 3000mah 15Amp CDR
AW 18650 3000mah 20 Amp CDR
As you can see, you've got several options for the Evic VTC Mini. The LG HG2 and AW may run longer per battery charge (may even be the same battery cell). For the Segelei, the Sony VTC4 would be best if you plan to take full advantage of its power.
I don't own a Joyetech Evic VTC Mini, but if I was in the market for a new mod this is what I would likely get. Nice small size with comfortable ergonomics, more power than I'd ever need, bypass mode (shutting off the processor to make it a mechanical mod should I wish), and using a replaceable battery (a big plus in my opinion).