Sub panel to in-structure shop questions. Details first, questions last.

St Louis MO city not county

3000 sq foot house built in the back of a 5000 sq foot, 1 story warehouse zoned mixed use but converted to Residential. (gray areas are fun)

The shop is in the front portion of building, but you have to go outside to enter the shop because we partitioned the building with an interior wall.

House section has a 200 amp panel + 100 amp sub panel (installed to reduce circuit length for receptacles, oven and dryer, not because the main is full)

The main panel is in the rear of the building but the ground wire is connected in front to a copper water main 115 feet away. The ground wire runs past where the sub will go. (pex plumbing throughout)

House's main panel power suckers: geothermal heat pump (no AC units!), stove top, 2 hot water heaters (one is only for backup heat for the geothermal heat pump and is never used, but I suppose you need to count it because it could be.).

Shop panel one way circuit will be 80 feet and will serve welding equipment, wood working equipment, ventilation, etc. This will be a one man show so I wouldn't expect to be welding at the same time wood is running through the planer while leaving the mill to cut chips, but I suppose a few fans, a tool or two could run at once while the lights are on.
Lets just say the maximum possible load would be:Three, 3 hp motors, some lights, fans and a small office with a computer plus a tiny hot water heater could be running all at once. If you need to throw a 30 amp welder into the mix as well, go ahead.

Questions are:
Biggest sub I can run?
Hopefully a 125.

What size wires? 2 hots, one neutral, one EGC, right?
I predict the hots and neutral will be #1 copper The ECG #4

What type of wire required for 1 1/2" plastic conduit that is already under the floor.

Do I need ground bars when it is technically inside the same structure, but you have to go outside to enter the shop? Can the bars be installed in the ground inside? (tall ceiling, so no problem with the physics)