You can make gas/petrol generators as large as you like, the bigger the alternator the higher the output, and the bigger the engine required to run it - plus running costs increase accordingly.
You don't want a 12V alternator and an inverter, you want it to generate the mains AC directly - they are freely available at pretty reasonable prices.
Certainly running an engine, low-voltage alternator, and an inverter would strike me as a VERY poor senior project. Your proposed engine also sounds much too small for the job.
Petrol driven welders normally create the welding voltage directly, they don't generate mains first.