Find a good local bike shop (ask around - not all LBS are good, and some sales people are worthless). The most important thing to make biking fun is getting a bike that fits well. How to fit the bike depends on the kind of bike you choose.
If you’re riding road and have no plans to ride off-road, a recumbent is the most comfy, although a bit more expensive. I don’t know anything about the crank-forward bikes, other than that I’d like to try one. The major brands (that you’ll find at a bikeshop) are all pretty good - the differences are mostly personal preference (e.g., relative frame dimensions, tube angles, etc.). Just try different bikes till you find one you like.
For most people talking about the kind of riding you do, I’d recommend a hybrid - they’re a bit more upright than regular road/mtb bikes, and hence a bit more comfortable. (I’m all about the comfort, baby - unless you’re wantin’ to become a racer-boi!) However, I’d hesitate to recommend a hybrid for someone your size. I’ve not looked at them in a few years, so they may have changed, but they were somewhat light-weight last I checked. (Most shops tried to sell them as women’s bikes.) I’d be afraid that a Clydesdale (mtb term for large guys) like you would crush the poor thing. If they’re sturdier now, then go for it.
Overall, I’d recommend a beginner’s mountain bike. They generally don’t have extremely wide wheels, so you can get a good ride on roads just by swapping out the knobbly tires for slicks. While you’re getting fitted at the bike shop, see about swapping out the stem and handlebars to give you a more upright posture (similar to a hybrid). Think about a comfy seat while you’re at it (probably have to pay to upgrade, though).
I’d also recommend a trailer for the offspring. You don’t have to worry about dumping the boy out or him getting into (too much) trouble; he can even nap back there while you do the work. I know people who regularly take their tot out on trails - she just laughs when the trailer soars into the air over logs/jumps/etc.
Pricewise, consider getting a used bike if the LBS has any. It’s often a good way to get a cheap upgrade in bikes. If you’ve got the time and energy, you can sometimes find good bike deals at pawnshops, but you have to do the research before buying or you’ll get something worthless. Check online for used trailers - most people I know bought theirs used and plan to sell it on once the kids are big enough. Lots of used trailers roaming the internets.