Yes, you can reduce the dia. of a boring bar, but there are limits first you have to look at what size cutter it has and realise that as you reduce the diameter you will also reduce the square hole, and lose clamping efficiency.
You can make a decent bar out of an old car drive axle, talk to a local car mechanic they throw them out all the time. you will probably need a carbide tool to cut it as they are quite hard, HSS will cut it if you go very slow and use cutting fluid. you can try using old broken centre drills as cutters, that way its easier to make the bar as you only need to drill a hole.
You can also weld small bits of HSS to the ends of a bar, done that many times to make a quick cheap bar using up old bits of HSS that are too small for any other use.
Also remember that as you reduce the bar dia. you must also reduce the length of stick out. to prevent bar flex and chatter. So in reality you need quite a range of bars.
You don'y say what size your lathe will be,
I generally advise with buying a lathe ,in fact any machine, get the largest you can comfortably fit in your shop space, without going overboard, also consider what work you intend to do, and always buy the best quality you can afford.
Good luck.