Help to choose the right bike multipurpose bike
From your question above, i would only suggest the following (doesn't mean I don't know about the other bikes):

Folding bike - for work and city/cycle lane/fairly normal surfaces only. You can also get away with usual city road hazards such as potholes and cracks (but not too extreme), also good weight support (e.g. laptop, clothes, etc.). You might find it a bit weird to suddenly switch to a folding from a normal road/hybrid/MTB. But overall, it is really great as my gf bought a Tern C8 last month(she is 5'4") and even I find it nice to ride (I am 6'3"). You can also carry it on the train and even on the aeroplane if you want. Some folding bike tyres are quite sturdy compared to hybrids so the bumps and holes can be ignored a lot more. I would still give a trial ride if I was you in order to be sure about the comfort. THIS IS QUITE PRACTICAL if you are just living a professional life and city-side commute with occasional shopping bags (about 6 kgs) behind you.

MTB (Mountain Bikes) - If you want it to use on a rougher surface as well as in the cities. They are a bit heavy, but can take poundings like no other. You could even go over some road kerbs that are raised by appx. 3-4 inches. I apologise to be mean, but if you are not young enough to handle the bike weight, you might feel it difficult to go around the hills with these heavy bikes. But if you think you can, Go for this one. My suspicion based on UK prices is that you can probably get a very good MTB compared even when you double the price (if you are lucky, you might get one with suspension springs too, COOOL).

It is also possible to attach some rack or similar thing behind your MTB so that you can carry weight such as your laptop and clothes to work. I never saw anybody doing it for MTB, but that really does not mean you cannot. 

Short answer is, if you are happy to sacrifice outdoor activity, folding bike is the answer. Otherwise, get an MTB, get rack, and voi la. 

Bear in mind that no matter what bike you buy, there is a maximum weight for that. I would recommend staying about 6-7 Kgs under the prescribed weight by the manufacturer/seller. It was never an issue for me anyway as I carried shopping on my folding and hybrid, about 6-7 kgs of shopping.

I am really sorry but cannot guide you about the US price. If any other user finds this answer suitable, but want to edit it to put the price information, be my guest. Normally, I would put the UK prices but this would be confusing as you said yourself that the prices and the types of bike vary in the US shops. 

Hope this helps. If you were interested in the brands at all: 
Folding - Dahon, Tern, Raleigh, Brompton (around $800 sometimes due to the high demand)
MTB - Jamis, Trek, Pinnacle, Raleigh (Off-road series), Fuji, Bianchi

The choice is now yours, If you think I can give you more information please post follow-up comments :)