Most of the time,for what you're doing, it won't make a lot of difference.
One thing,though,some of the stuff they sell as RG59 these days is nothing like the real thing.
"Real" RG59 is quite flexible,has a fairly dense copper shield,a copper inner conductor and an outer PVC sheathing which doesn't move around w.r.t the rest of the cable.
"Pretend" RG59 is stiff,has either an aluminium shield,or a fairly minimal copper one combined with some cruddy aluminium foil,a copper plated steel inner conductor,& the integrity of the sheathing is poor.
It may not fit BNC connectors made for the real stuff properly,with resultant loss of signal at embarrassing times.
RG58,by & large,is a lot closer to the original article.