Mont Blanc is doable if you are fit and athletic. Preferably also have some backpacking and outdoors experience. That is predicated on you hiring a guide to teach you some skills before heading out, as well as sheperd you to the top. Do not go up it by yourselves without knowledge and experience. Even with a guide, you might get weathered off, altitude sickness, or lack of fitness. I climbed it with a friend last summer who was new. He can run 2 miles under 12 minutes and do 25 pullups (very fit), and he had a lot of trouble with the last few hours. I found Mont Blanc, even by the "tame" Gouter route, more challenging than I was expecting from reading some of those same websites you mention.
If there are 8 of you, even going guided on the Gouter route, I would expect that not all of you would make the summit, even under ideal weather.
The Eiger is not a place for new climbers. Even guides insist on a 1:1 ratio, so each of you would need your own guide. But don't do it. It's not a place to find out members of your party are uncomfortable with extreme exposure while on rocky terrain in crampons.
Late May and early June are also early season for many climbs in the Alps. You will likely encounter snow and ice, and many routes might not be passble.
I don't know anything about Kili or Fuji, other than they are tamer "walking" peaks, which might be more appropriate and have some name-brand appeal. I've heard that taking a safari after Kili is a great thing to do and a life-list trip in itself.