I agree with Tanza on the solid privacy fence, the higher the better. Nexa can jump our 6 foot privacy fence and only touch her front legs on the top. She only does it when there is something to chase, or if one of the neighbors dogs get out. Last week I installed 2 foot mesh at a 45 degree angle around the entire top of the fence. So far it has worked great.
Go with the max you can… and see what happens... not all are jumpers.... and usually when they can not see what is on the other side, the "need" to get over the fence drops.... If necessary you can go with a hot wire on the bottom and top..... one zap of the wire is usually enough to get them to think better of trying to go over the fence. It is the same type of hot wire that people use for horses and cattle and sheep/goats etc....
We had 4 ft fencing when we stated out with rescues, but kept them on a lead until we could trust them outside. BUT they were never left outside when we were not home, doggie door was installed, and the block was put up until we got in…mostly, they wanted to be with us.
Now we have a 5 ft chain link fence with lots of bushes around them...but I have not found my 2 b's want to climb or excape..
WE walk them 2 - 3 times a day for at least a mile.
We make home too nice for them to try to go...
BUT I do hear others are major climbers, so that should be considered.
We had a cat for years and quickly learned if he was out at night he came home bleeding 50% of the time so he came home at dinner to be fed and we locked the cat door with him inside the house. I sounds like basenji like of breeds are best supervised always - which is not a problem - but I know I can't out run one heading over a fence so I need a second line of containment. The contractor just came by with the property line info. I need to let him know what type of fence ….. I’m off to walk the neighborhood (with my imaginary basenji) to see what styles there are which are high enough.
We have regular ol' field fencing, maybe five feet high. It'd be really hard to climb because of the wire, spacing, and flexibility of the fence. Neither shows a desire to try beyond standing up on it when something really interesting is happening on the other side.