For a drop-in plug-and-play solution, with money to spend, I'd probably ask Cell-man what he's got in A123 20Ah prismatic packs.
For DIY reliable and sourceable parts, I'd go with A123 20Ah prismatics. Given they're 20Ah, if you set yourself a limit of 16Ah, you will almost certainly never unbalance the pack far enough to need a balancing BMS. I would bulk charge, and simply periodically (monthly? bi-monthly?) check the cell voltages at discharged state and at charged state with something like a set of Battery Medics or Celllogs, just plugged into a connector for this purpose when needed. I'd keep one single-cell charger around for any cell that ever did get out of balance. A123 modules are available pre-assembled that you could "hack" to do whatever you want, and probably reuse the cell-mounting hardware, just rewiring it to your needs, more or less.
For the same thing with even better cells (higher voltage per-cell so less total cells for 48V (~60V full), I'd go with EIG 20Ah prismatics. The catch is these are nearly unobtainium. Jay64 got some via an unnamed source, but that's the only known pack of this type on the forum. I think some commercial EVs use them, too. Sangesf was organizing a group buy of these things at one point, but it fell apart and that's the last of that I know of. I don't know if the source he was getting them from was ever made public; if it was you could try to get some directly from them. Methods LVC/HVC setup can be used directly with these cells, for overcharge/overdischarge protection. (not with the A123, though--different cell voltage)
If you don't mind the extra work of first cycling and verifying all of your packs/cells, and either repairing or tossing any that don't work as expected, and then paralleling several packs for each of several sets, and then seriesing those sets together for the voltage you want, RC LiPo can also do what you want well enough. Methods' LVC/HVC setup can also be used with these (it is in fact designed for them, including being made to parallel the packs for you). Then just like the other packs, you can bulk charge, periodically check cell balance, and top off any low groups with a single-cell charger.
I don't know what the cost for any of these options is, so they might all be out of the $1000 budget. But if I had money to go buy new stuff, and needed a pack, one of these is what I'd do--almost certainly the A123 or EIG DIY packs.