I recommend the 4mm ID/8mm OD for beer. Works great at 5 to 6 feet in length for typical ale dispensing. Perfect pours here at 6' and 11 psi at the kegs for all my "normal" ales, and at 9' and 15 psi on my higher carbed beers (like the raspberry hibiscus wheat I have on that tap).
If you need longer lines than say 7 feet, you might be better off with the 5mm ID/8mm OD, which you can treat almost like conventional 3/16" ID beer line, where the rule of thumb is one foot per psi of CO2 - though I'd add another couple of feet to start as the EVAbarrier tubing is definitely slicker than solid PVC tubing.
For the gas side you can use whatever works for you. 4mm ID would be fine. I went with 5mm ID just to make getting over my existing barbed manifolds easier, but I could have still used the 4mm ID, it just would take slightly more time/effort.
Basics come down to two things: proper carbonation, and proper line lengths. For the former, always reference a carbonation chart or table or calculator to determine temperature vs pressure = carbonation level. A favorite here is this table:
Force Carbonation Chart - Kegerators.com
For the latter, reference the only beer line length calculator worth using:
Determining Proper hose length for your Kegerator. Plug in your particulars and it will spit out the minimum line length to use.
Beyond those two concerns lies a boatload of little things, like running a small fan 24/7 to prevent temperature stratification, coiling lines atop kegs so they don't droop and collect gas bubbles or freeze against the keezer walls. And on and on. Might find some "similar threads" below worth perusing, but for sure there's a ton of info on keezer builds and operation here in the forums...
Cheers!
