TT-length-wise, traditionally over the last 15years frames were under the 19". Things did change a bit lately with street-esque riding infused into pure flatland routines and that drove TT-lenght to as much as one and a half full inch but, fads and trends aside, I would stay that 19" is the sweet spot for taller riders +6' and 18.x for shorter riders is the best compromise between comfort and manoeuvrability but having said that, those sizes are actually the more common on the most recent frames released so you can't go wrong.
The used market may be a valid option but thread carefully because it can get very expensive very quickly to build a bike from parts instead of buying a beginner setup.
If you live in the USA the market is plentiful but otherwise you will have to wait for the good deals to pop up.
Weight-wise, if you care about that, some good options are bar-stem combos, A Bad Thing and KHE (SwissMiss) have them, In Europe you can get them below 60$ and that will save you, depending on the parts you had in mind, a good 1.1lbs (500gr). KHE makes a very light tire too, the MAC1, not cheap, but at less than 0.6lbs (300gr) you can easily shave off another 1.1lbs (500gr) if you get them on both wheels (some riders complaint they are not durable, I use a rear one with zero problems but I am a front-wheel rider). Those two things alone can save you as much as 2.2lbs (1kg) which is a lot on a BMX bike.
Anyway, weight is not important, you will always weight a lot more than your bike and leverage will always be there as soon as you start throwing your body weight around, the bike will always feel featherweight in comparison so I wouldn't worry and the riders who do (me included!) should go out and ride more instead of constantly keep worrying and spending money on lighter components...