Depending on the type of agreement you have with the other person/s , sometimes access to the miner is not required per se, meaning that the owner of the miner will be sastisfied with just watching the hash-rate on the pool side, while the host will take care of any updates that needs direct access to the miner, on small scale this works just fine I have seen many people do it this way.
if however access to the miners is a must then here are some options.
1-Remote desktop.
2-VPN.
3-Port forwarding.
you need to DYOR on each and see the pros/cons , if you go with VPN consider PiVPN installed on either a Raspberry Pi or a cheap PC.
for 10 gears, you will need at least 11 ports on the switch , keep that in mind you always need gears number + 1 or +2 if you want hook up any other equipment such as a Pi or a PC, so go with 16 port.
If your modem is capable of routing ( probably is ) then you don't need a router.
in the near future I will make a "Step by Step" guide on remote access to miners and privilege management, no promises as of when , all the info you need are available online tho, so the guide will be made just to make other people's life easier.