Pre-Dominiom war when everything is pretty chill. Starfleet kinda seems fun until you realize that you have to basically do military training and all this bullshit to join and then you gotta go die in space half the time. I'd maybe just try and get a runabout or the equivalent and just sorta wander around with some pals and look at totally safe and previously explored space things. I would also open a Volcel Precinct on Risa.
There's stuff like the Vulcan Science Institue and other ventures that fall under federation jurisdiction or 'funding'. Lower Decks had that recruitment day episode that shows a whole bunch of the space weirdos with spaceships are part of some kind of guild or whatever.
Transporter technology and the fact the average Starship can depopulate a whole planet makes in-atmo ships kinda more trouble than their worth. But there are plenty short range vessels that aren't ftl capable. Impulse in tng can get you pretty close to warp 1 anyway. When they're Starship they're called that because they are capable of interstellar flight. Thst being said, Quark also makes a big deal about getting his own warp capable ship in Little Green Men.
At this point I feel like the best way to get a ship is to become plot relevant and hope it's a lighthearted one off where you fly away sage at the end.
That is such a fucking gamble
Stsrfleet is Q's way of testing random weirdos with spaceships when they venture too far.