You already HAVE the lathe within your reach ... and you are asking those CANNOT reach out and touch it?
Just go and look.
You don't need - or even WANT - a "live" center in the
spindle. They are for the tailstock. 2 MT, usually. Ten bucks for a Chinese "dead" center? They work OK. Spend more for a Stark or Riten when you know more.
Import "live centers", same again. The cheap ones are. Cheap.
The good ones are NOT cheap. Skoda is value for money. Riten is worth their premium price. IF you have the need for top-grade and long-lived.
You can turn between centers "real, soon , NOW!" by MAKING a center at the headstock/spindle end on a short length of stock gripped in any chuck or collet you already have.
As it turns WITH the work, some modest pressure is applied, but
no sliding friction, so it need not even be hardened.
TS dead center. OTOH, should be
seriously hard. Several of my "working" ones are Carbide tipped. Some very finely finished all-steel ones are NEVER used for turning. They are kept safely put away and used only for measuring & alignment.
A store-bought or shop-fab "driver dog" can have it's tail rest against a chuck jaw and you are "in bizness" rapidly & cheaply.
Light lathes, SB especially, are generally just fine with "dead" centers at the TS. I also recommend a squeeze-tube of "pink slime" AKA CimCool "center saver" for lubing a dead center. Nothing is perfect, but it IS "closer than most".
Live centre "kit" wih multiple tips that cover pipe, tubing, and such CAN be handy as much for that variety as for having roller bearings. Start cheap. You probably won't even use it often, and even then, if you invest in BETTER goods, later, the El Cheapo is still there for less demanding or riskier setups or tasking where you might want to modify something.
2CW