The way i upgrade is: group level > group skills > group wheel > group activities. It's up to you if you upgrade skills or wheel first, skills give a small power boost while wheel will result in few coupons more on average. I'm leaving group activities for last upgrade, because the only thing that changes here is a small boost in gold- not much in comparison to power or getting cp. Level those things up in a priority you choose as soon as you can, no point in stacking up group contribution until you can level all things up at once. In order to upgrade group level, you need to upgrade all others as well to the same lvl, so it's only a matter of order.

you may want to take vote's and see what your group mates want to upgrade(skill study is you best bet to get more power)

As a leader of a group.. I upgrade my group this way : Group Summon(serpent max level) > group level > group skills > group wheel > group activities..

is the group summon really worth leveling seems really expensive for no real value to me

Yes,

1. Snake does give you extra BP to your team

2. Good for GNW, can be used to outplay another team.

3. It can work as shield to block mystery from your opponent.

But you can get the snake maxed w/o using group fund... it would take a while but you could. So it's quite a case of "pay to get early".

Mind, with the 3 field now, snake is much more significant. Back in the 6 field days I would have strongly adviced against it as it doesn't do much half the time due to opponent not stationing in the field it is in. But with only 3.... there might be value in getting it earlier.