So I need to replace or rebuild my generator. Should I just take this opportunity to get a new generator that is a combo generator / inverter ? Or is there even such a thing as a combo unit.
New generator will be expensive. You should have your current one diagnosed to understand why it's not operational.
First, a baseline. Generators only create AC power, 120vac in your case. . That's it. They burn some sort of hydrocarbon (diesel) and there is NO conversion to or from 12vdc. An inverter converts 12vdc to 120vac household power. That's it. They come in a variety of sizes from small 60 watt ones that plug into a cigarette lighter, up to hard-wired inverters that can power an entire house for solar power applications. A battery charger takes 120vac and converts to 12vdc to replenish (i.e. Charge) a battery. For boats, inverters are often combined with battery charger into a single appliance. A typical sized one on a boat your size would be around 2000 watt inverter with a 55-amp battery charger. Purchase price would be around $1000 with professional install costing around that much with cables and fusing. Right now, your boat already has a battery charger somewhere that operates when plugged into shore power or when generator is working. You also have an alternator on your engine that charges when you are underway, though depending on size of batteries, could take many hours to replenish a charge after a day or two at anchor.
Before you make any decisions on buying stuff, you really need to think about how you will use the boat and what problem you are trying to solve. If you have an electric stove, you need your generator. If you want air conditioning, you need your generator. Everything else can be run off your batteries, just depends on how long you can sustain the system. A GB 32 is a pretty small boat and most folks use these as a day-boat or occasional overnighter. That said, I once owned a Willard 30 and used to take her on extended trips of a few weeks.
If your boat runs entirely on 12vdc (fridge is 12vdc and stove is propane), then your only need for 120vac is likely to charge your PC or perhaps run a TV. This can be done with an inexpensive 300-watt inverter that plugs into a cigarette lighter. A microwave typically needs a 2000-watt inverter due to startup draw.
So you have to decide whether you want to just power individual loads such as charging your PC (inexpensive), or if you want all of your AC outlets to be powered while underway (an inverter charger - relatively expensive and more complex).
Sounds like the boat is new to you and you're just getting started in the wonderful world of boating. My gut-level recommendation is to figure out the generator repair, then do base minimum for an inverter and not go the full system-wide inverter/charger route until you've owned the boat for a while. Also, check your battery bank capacity and age of batteries.
Good luck and welcome aboard. Nice little boat.
Peter