First, are you sure that 30A is a sufficiently large breaker for your range circuit? Most electric cooking appliances (freestanding electric ranges, cooktop/oven combinations) require a 40A or a 50A circuit.
The 20A breakers do sound correct for the lighting and receptacle circuits, although you will need more of them, as every dwelling unit must have at least two dedicated 20A small appliance branch circuits and a 20A bathroom receptacle branch circuit; if laundry facilities are present, yet another dedicated 20A branch circuit must be provided for the laundry room outlets. You will want to use a double-pole breaker for HVAC, though: all but the very smallest HVAC appliances require a 240V circuit, and this includes packaged terminal units, even though they only draw a relatively small amount of current (<20A) compared to a conventional air conditioner.
The overall capacity of the subpanel you have on hand (100A) is more than adequate for an apartment-type dwelling unit; however, you will want to check the number of breaker slots available to you in it -- full-width slots are at a premium these days due to AFCI requirements, which makes depending on tandem breakers to fit all your circuits into your panel quite unwise.
Your #2 wire will be adequate for the feeder conductors provided it is copper and of a 75°C rated or better insulation type (such as ordinary THHN/THWN). If you are using aluminum wire, I would upsize to 1AWG -- 2AWG aluminum is marginal for 100A service, requring 90°C rated insulation in order to be at all usable in such an application.
You may feed a 14-50 outlet directly from your main panel since there are unused breaker slots available. Use the correct breaker of course, and correct conductor type/size for the load. Do not forget voltage drop and temperature ratings when choosing cable.
You do not need to add another sub-panel for a single outlet.
Do not expect the code book to tell you what you can do. It's there to tell you what you can't.
Best Answer
To answer your question, the smallest sub panel you can find. You would need to use conduit and correct fittings for running wire. However, I wouldn't buy a sub panel for just one double poll breaker. Instead, since this is a sub panel we're talking about here, I would set up a two or three breaker sub panel. 1 or 2 for the lights and other outlets, and 1 for the RV outlet. For the RV outlet, if it is a 120V outlet, which I think it is, they make up to 50 amp single poll Square-D breakers. Although, you would need a 40 or 30 amp single poll. For the other breaker(s), I would use a 20 amp. Just a suggestion...