Migrating 10/100 to 10/1000

I have a peer to peer WAN network two LAN connected via VPN.

All devices either run on 10mbps or 100mps.

If I move site a that as two switchs one upliked to the other to be using two 10/1000 copper switches would I be able to still run my network if I dont change anything.

Then If I wont to run certin devices at 1000 all I would need to do is install 10/1000 nics.

Also I use a 10/1000 VPN hardware router also for internet access. Will this be effected?

What cable ratting do I need to run for the cabling? Cate 5E or Cat6 etc?

Any tips on what setps to look at to migrate to 1000mbps.