For a Mini Provari, I recommend 4 batteries at a minimum to be be used in rotation. The red Aw 18350 IMR's I use are rated at 700 mAh, but if you use any voltage range higher than 4.2 volts you will get less than 7 hours use on one battery on average.
Batteries : AW IMR 18350 3.7V 700mAh
I recommend the
Nitecore i4 Intellicharger so that you are able to charge more than 2 batteries at a time.
http://www.rtdvapor.com/online-store/battery-chargers/nitecore-intellicharger-i4-detail
An alternative would be the Xtar WP6
Battery Chargers : Xtar WP6 II You will need additional spacers to fit multiple 18350 batteries simultaneously if you choose this charger.
Battery Chargers : XTAR Charger Spacers I have this charger and in hindsight I wish that I had gotten the Nitecore version because the coiled springs in the battery slots are flimsy and the 18350 button top batteries are just a tad too long to stay in place even with the correct spacers (I have to lay something on top of the battery to keep them from popping out).
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My preference for juice delivery devices are
pyrex cartotanks such as the IBTanked
IBTanked - Get Tanked With Us!. If you've not used a cartotank before, they have a slightly higher learning curve and take a few more minutes to set up than a clearomizer or clearotank will. But I have found that they allow for more flavor production than the string-wicked devices. For a Mini Provari I recommend the 19mm diameter XL length IBTanked, or if you prefer higher juice capacity go with the 22mm diameter and get a Provari Pro Ring
http://www.e-cigarette-forum.com/forum/provari/383572-provari-pro-rings.html
I've done an extensive review of the IBTanks here:
http://www.e-cigarette-forum.com/forum/blogs/baditude/3318-3-ibtanked-pyrex-glass-tanks-review.html
I've done a cartotank setup guide here:
http://www.e-cigarette-forum.com/forum/blogs/baditude/3710-5-cartomizer-tank-setup.html
View attachment 230387 19mm IBTanked

22mm IBTanked with beauty ring.
Only the cartomizer in a cartotank need be replaced periodically, and can be expected to last for about 15 - 30 ml of juice. The tank itself can be refilled multiple times. Once the draw becomes stiff or flavor production degrades, replace that carto with a new one. Pre-punched cartomizers are pretty cheap - about $2 each. Just be sure to get the correct length of cartomizer for the length of tank you have.
http://www.e-cigarette-forum.com/forum/blogs/baditude/3295-2-sample-list-vendors-selling-pre-punched-single-coil-cartomizers-cartotanks.html
View attachment 230393
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A
Kanger ProTank is a clearomizer tank that also uses a pyrex glass tube. If you go the clearomizer route it would be my first choice. It would be a little easier to use (easier fill method) than a cartotank for a beginner. The inner head is replacable to prolong the usefulness of the main tank. I have found these to give adequate flavor production, but not on par with a cartotank.
I've not tried the Kanger Evod clearomizer because to use on a Provari (510 thread) you need an adaptor (510-ego thread). I've tried the Vision Vivi Nova; it is top coil/bottom fed, meaning it gives a warmer vape (I prefer cooler like the bottom coil clearos) and because it is a top fed wick requires frequent tilting to keep the wicks wet to prevent dry hits. I also prefer the looks of the Kanger ProTank on my PV's.