At some point you may very well need that resaw capacity, but there are other practical benefits to a larger saw.
One is throat depth, meaning a larger one typically gives you more room between the blade and the frame making it easier to work with larger stock.
Another is the wheel diameter, larger saw has a larger wheel diameter so it bends the blade less, the less you flex a blade the longer it will last.
The larger saws also tend to be built better and have more feature, like a easy to use blade tension release. If you don't use the saw regularly (or even if you do) you will want to release the tension on the blade which in theory is good for the blade and the saw.
Same with guides and tracking adjustments, larger more expensive saws will likely have better longer lasting setups.
I guess it mostly depends on how much disposable income you have, and how much you end up using it.
A well tuned nicely set up band saw is a handy item to have, but with woodwork there are generally many ways to accomplish the same thing, so if you find you like the bandsaw you will use it often, if you don't like it you will make cuts another way.
Say for instance those Adirondack chairs you are thinking of. Lots of different styles fall under that classification, but lets say you pick one that has tapers on the outside back slats.
With a decent bandsaw setup and some practice you could mark out the taper and cut it quickly with no additional setups and it would only need some minor sanding if that to be on par with your other cuts.
Alternately you could make a taper jig for your tablesaw and use that, or use a circular saw, or a jig saw (likely to need more sanding though) or a handsaw or a hand plane, it can also be done with a jointer if you like using those.
Another consideration, at least for me would be the other tools I have. If my other machines are good quality and capacity I wouldn't want a crappy bandsaw - and I'd be much less likely to use it.
On the other hand if I have relatively low quality machines it wouldn't make sense to have a really expensive bandsaw (unless the majority of my work was done on it) although it would most likely get used proportionally more.
Personally I would look for a decent used saw at least 14" and in good shape for a reasonable price. That would match my other machines and be in line with my budget, and I'm about as likely to use a bandsaw as another machine depending on the cut in question.
You do want to watch the older used machines, a lot of them are wore out. If you have to buy new tires for the wheels, and new guide parts, or bushings then you might be getting close to the price of a new saw. Or even worse the table is warped or the motor is junk or goes out in a couple months, etc....
