Welcome to permies! If you build a
rocket mass heater according to best practices, you will never regret it. Building in the basement is generally not a good idea, unless it is a main living space where you will be in sight of it for a few hours a day. A J-tube RMH (the simplest and easiest type to build) requires reloading every half hour to 45 minutes. A batch box holds more wood at a time and may only need to be fired once or twice a day, though it requires more skill and expense to build the firebox. Basement locations may also suffer from competing draft issues, depending on circumstances.
Size depends on your home size, insulation value, and climate. A modest home in a relatively mild climate will probably want a 6" diameter system, while cold climates or larger, leakier houses will need an 8" system. (A 6" batch box delivers as much heat as an 8" J-tube.)
Incorporating existing ductwork is generally not done, and would be a real engineering job. I would not try it unless you are familiar with those systems. For most systems you want a 55 gallon barrel if you are going to use a barrel at all. Newer designs often use a hollow
cob or masonry box called a "bell" for heat exchange and thermal storage. If you have a long mass bench oriented so it runs across a lot of floor joists, you may not need any reinforcing, or only minimal added support. If you use a more vertical and compact bell, it will need masonry support down to the basement floor.
Galvanized stovepipe can be used from the mass up to the chimney through the roof (which is much better than a chimney through the wall), as long as you do not use it close to the hot core so as to avoid toxic offgassing. Heavier black stovepipe where it exits the mass and is subject to impact will be safer.
If you do not have it yet, I highly recommend the
Rocket Mass Heater Builder's Guide by Ernie and Erica Wisner for solid proven techniques and designs. If you are interested in batch boxes, look at
batchrocket.eu for complete information.