Here is the reply that I got for Coinbase.com
Im not sure if by generation transactions if you mean newly minted coins? If that is what you mean, then yes, we do support them, but like any newly minted bitcoin. youll need to wait 100 blocks before you can transact with them.
I hope that helps! Let us know if you have any other questions, and thanks for using Coinbase.
That still don't tell me if it is good or not, now I started Bitcoin Core in pruning mode and again it is a lot a bandwidth, MY ISP allow me only 130 gig a month
Is there a alternative wallet ? I would like to go back to solo.ckpool
I'm pretty sure you could get by with a light wallet like Multi-bit and be fine. That still lets you control your coins, but you don't have to run a full node to make it work (IIRC).