First of all, share only that which really needs to be shared. Even in a peer-to-peer network, it is easier to manage the access rights by using groups. Use the strict group policy throughout the entire network.
Considering the fact that a peer-to-peer network should not have more than ten computers and there are also ten "admins", give them the appropriate education.
Is there a need that all computers provide shared folders? Is a centralized backup not better? In that case, one workstation should be more powerful than the others.
The double of RAM and a second HD is still better than nothing. This powerful machine shall be the "network server". There is no need to buy an expensive license for a server, due to having only ten workstations. Remember, a workstation allows ten incoming connections at the same time.