As far as I know you can fly via Frankfurt directly to Min Vody but most people go through Moscow (good reason to spent a day there!).
As for Pilgrim Tours, I joined them last year and they really did a very good job, everthing was organized very well and the guides speak perfect english.
You will need crampons, ice axe, harness and isolated boots (plastic boots but I managed with my Scarpa Cumbre boots). On their site is the complete equipment list. They also rent some gear, might be interesting, it's also on their website.
The food on the mountain is very good and the Barrels are very comfortable.
I hope you will enjoy it as much as I did.