We can ALL tell you what we have for fence, what has not worked and what is (?) working. You can choose the best you can afford BUT it does not mean that you won't have any issues ever. You may not, then again, you may. Size of goats may be a consideration for "some" of their escape attempts.
I use 2X4 no climb woven, 4' tall. MOST of the time it is just fine for 99% of my goats. This year I have a very athletic young doe who sized it up, takes 3 steps back, one up & propels her lovely self over the top like a deer!

None of the others do this. I hope she will stop once bred and in milk. I find the does in milk are FAR less intent on escape tactics that may injure their udder. (This girl goes back in same way).
Now my buck is huge & while tame and content, if in rut he will challenge ANYTHING that is called "fence". Cattle panels keep him contained but he continually pushes on it to find "the spot". Summers? A plain old 4' fence is fine.
None of mine leave my farm when out...even if thru a gate left open. They graze and forage -- there are those tree, bushes, flowers, gardens issues!! -- but, stay fairly close to their barn areas. In fact, I can open a gate, call them and they will follow me like the Pied Piper! I have taken them to my furthest fields this way often. However, when thru eating, they all rush back "home". If I want to KEEP them in a further field for the day, I must shut that gate. When they want back, they look for an escape to come back..
Goats have personalities and HABITS. They are creatures who want consistency. If you milk, do NOT go out of order

They know their order & don't appreciate a change....although they may rush to get in because most are fed on the stands.
SBC is correct about testing. Proof of testing is best for all parties. It's less expensive that vets/meds to cure (if you can) or losing your herd, as others have attested.
Goats are awesome animals. Everyone is giving you some great info to make your ownership experience a good one. We love all of our goats -- you will love these amazingly smart and affectionate animals. YES -- very smart!!