The least expensive starter kit that I've seen is still the
Riva lite bundle (even less expensive than the regular 510's) for only $30 when you click on the 20% discount banner. I am not affiliated with any vendor, this is just my genuine advice.
Also, I highly recommend against trying to share one kit between two people. At some point one or both of you will be waiting for batteries to charge. At bare
minimum you should have at least one extra battery on hand to share (and if it was
1000mah, that would be even better).
As for which method is the best; the top two vaping methods are drip tips and cartomizers. Most people use both. If you are on a tight budget I would at least add a
drip tip or two to your order because cartomizers are considered disposable so they will need to be thrown out and replaced often but the drip tips will last forever.
Vaping will end up saving you money over smoking very quickly so you'll be able to try out cartomizers and get another kit (or whatever) pretty soon with all the money you'll be saving.
You'll probably like juices that are about 18mg and made with more VG and he'll probably like 24mg and more PG -- this is just if I was forced to predict -- but you can never tell how it's going to work out until you jump in, so it's always best to get a variety and see how it goes. The average vaper uses about 3ml per day so you'll want to get enough to last a couple of weeks and by then you'll have some idea of what mg to get next time and what flavors you like.
Good luck!