I don't know if you need to put another spike in the ground, the main box is already grounded to earth and any additional boxes would be. If your 20 seems overloaded, then likely you would need a sub panel (I won't need one, my box has a lot of open breaker slots, and I have 200 amp into the house). In terms of what size breakers, that depends on what size wiring you use, since you are wiring new I would use 12 gauge Romex and that would allow for a 20 amp breaker (that is code). If you happen to have a ton of 14 gauge romex you want to use, then use 15amp breakers and have several circuits, will give you the same thing. Having several smaller circuits means you would need to wire those circuits, extra work. I would likely wire 2 20 volt circuits rather than 3 15 amp circuits, 2 20's would give me plenty of room for expansion and I would need fewer UPS's to cover all my train circuits.
One thing to be mindful of is total power consumption in the house. Doesn't sound like that is a problem now (if you are running everything over a single 20a circuit, and it doesn't pop, and the main breaker doesn't pop, you likely are fine), but if you are planning on adding more power draining devices you might want to take a look at the size of your service and see if that needs expanding (likely not, most houses these days seem to have 200A service, but older houses may be 100).
As far as filtering power, I would use a UPS on each separate circuit that powers your trains (right now you have one). Verify that it is the type of UPS that powers off the battery continuously and charges, not one that cuts in. Not so much for the back up power, but rather as far as I know that gives the best voltage clamping, that the battery----inverter-----outlet is going to be the cleanest . You would need to find a UPS with the wattage to handle a 20amp or 15 amp max circuit (2kw or 1.5 kw, respectively), but the good news is they aren't ridiculously expensive. You don't need a heavy duty that you would use on a sub pump or the like that will last for hours, you really only want it for the voltage clamping I would presume. I have used APC UPS units I got for like 100 bucks at CDW and they have kept my sensitive electronics protected. At one point I kept burning out cable modems and my wifi routers with power surges (the power in my area was incredibly dirty at the time), once I went to UPS, everything has been fine.