I'm 5'6". The size chart at bikeexchange.com says I should get a bike with a 16-17" frame size and a 27.5" wheel size. If the bike I buy is delivered, I don't want to make a mistake. How much flexibility is there in these ideal sizes?

You don't say where you're located. Go to a few bike shops and test ride a few bikes and see what the staff recommends size wise.

I did and the guy said forget frame and wheel size, but instead focus on geometry. He said the standover should be 5'4" and I needed a short top tube and long head tube because I don't want to lean over that much. Like I said, the bike will be delivered, since I'm getting it from Ebay or Facebook Marketplace, and I don't want to get the wrong bike.

I've learned standover is just one measurement, and agree that you also need to worry about the reach. I'm a good example why those charts are only a starting point. I'm 6'-2", which Trek's tables say is an XL frame. But I have short legs (31.5 inseam), which the charts say is a medium frame. Combining those dimensions in the Trek calculator gives a large frame, but some of their large bikes have standover heights that are uncomfortably close to my inseam, others are less tall. The reach varies as well. So I'm going to have to test ride, and that may be months before they get something in stock. The new bike I want (the FX 3) isn't in stock until April.

In your case I think you are going to have to look up the specs of any of the used bikes you are considering, and then maybe get some help on the Fitting Your Bike forum here (sorry, can't post a link because I have less than 10 posts, but just search under Bike Forums).

Mark

Find a local bike shop and throw a leg over the nearest thing to the eBay bicycle, then take it from there. You have have a short or tall inseam from the "norm" of your height. Your arms may be longer or shorter from the norm. Your preferred riding position may vary from Tour de France to the local party ride with you lounging at the rear of the pack. Ignore knee over pedal, and cleats offer a centering position to start from.

I've always been skeptical of the "geometry is everything" approach, unless you're a racer. Reach, at least, is adjustable with stem and/or handlebar choice. Standover is written in stone.

PurpleJersey , when in doubt, consult Sheldon Brown, who has this to say about frame sizing. HTH.

EDIT: I should add, as a fellow short rider, that for anything but racing it's hard to go wrong with a '80s to early '90s steel mountain bike. The 26" wheels are proportional to our size frame, so no tortured geometry to squeeze too-large 700c wheels in there. They're also extremely versatile (as long as you stick with a rigid fork) too; they make great gravel bikes, commuters, tourers, grocery-getters, whatever you need. My commuter/explorer is only limited by the engine:

I paid a high end "Britain, Italy/ and Titanium custom bike builder to "your geometry", and spent 4-hours riding their machine. While we were having coffee, we talked and I looked forward to getting my "Custom-Fit" from Seven cycles in a Titanium Gravel bike. 4-weeks passed and the local shop owner informed me that Seven would not release my fitment to me without an order for a Ti bike. Then the owner refuses to return my $100-dollars because I was not going to buy a titanium bike from him. I contacted Seven and he said that the owner had never contacted them, turns out that when the bike shop owner found out that I was not interested in purchasing a bike from him, he figured that $25-dollars an hour was just too much to loose. I raised #@$^Q#$ in the shop with an animated overly loud voice.... The till opened as he left the shop, with instructions to refund my $100 dollars.

The culture of a significant number of shops is sell, sell, sell and so the advise to visit Sheldon Brown's site is well respected. Don't buy into the Leaner! Stronger! Faster! snobbery bike fitting software.