How does frame size and wheel size play a role in choosing the right size of bike?

Here is the thing.  You can have small bike wheels on folding bikes.  Mountain bikes come in three wheel sizes.  26", not made so much any more.  650b (27.5 inch) and 29.  The reason that 29ers came into style was the 2012 Olympics where the larger wheels dominated the mtb events.  The 29 is able to go in a straight line quickly, but loses out to the 26 on maneuverability.  So they re-introduced an older European size, the 650b, as a half way between measure.  A bit of the 29s rolling speed and some of the 26s stability.  So wheel size does not measure the height on adult bikes.  Children's bikes, its all about wheel size.  So adult bikes are measured in frame size.

Luck

Most sizes (usually ALL sizes) of a particular model will use the same size wheel and tire. Occasionally, a very small frame (much smaller than you would use) will have proportionally smaller wheels, which makes finding new tires more difficult. Someone over 6 feet would usually ride a normal bike with normal size tires. If you're looking for a hybrid / city bike, almost all of those will have tires described as 700C with different widths (fatness) from about 20mm to 50MM marked on the tire as 700C-30, for example. Those ALL have about the same diameter; around 27". There are many mountain bikes with knobby tires with weird designations like 29er, 27.5, etc. For some reason, bike manufacturers like to dream up new designations for older sizes that can be promoted as the new miracle size. Be sure your new bike has 700C wheels. The tires will have 700C or 622-xx (where xx is the width) molded on the sidewall. Buy it from a real bike shop so you have a reliable place for service and you'll get one that fits you properly. Happy riding.

Most racing bikes and commuter bikes do not have a suspension unless you call those little springs under the seat a suspension.   Bigger wheels smooth out the bumps so you go with the biggest wheels you can.  However if you get a bike with front and rear shock absorbers then the wheel size does not matter as much.   You can get a small wheel bike with a big frame and let the suspension take the bumps.   

Discount stores measure bikes by wheel or tire size.  WRONG!  Adult sized bikes from a REAL bicycle shop will be measured by frame size.  If you're 6' 1" tall looking for a hybrid/city bike, I can just about guarantee they'll all have 700 X something size tires...700 X 32c - 700 X 35c - 700 X 38c, etc.  

Know how to choose the correct size bike?  In all capital letters...QUIT LOOKING ONLINE!  Go to a REAL bicycle shop & TEST RIDE as many as you want and/or can.  You may have to leave collateral, such as a drivers license or credit card - but TEST RIDES ARE FREE!  

Why are test rides so vitally important?  Because frame sizing from one company to the next is NOT universal.  An XL (or 21" frame) from company 'A' might be measured different by company 'B'.  Some measure from the center of the crank all the way up to the very top of the seat-post tube.  Some measure from the center of the crank to the INTERSECTION where the seat-post tube joins the top tube.  That could be an inch or more difference.  Read all about frame sizing from the late cycling Guru, Sheldon Brown on this link... https://www.sheldonbrown.com/frame-sizing.html 

If you're thinking about buying online...here's one word of advice.  DON'T!  A) What guarantee do you have there won't be hidden damage inside the box?  NONE.  B) Who assembles & tunes-up the bike?  YOU!  Or you pay a bike shop mechanic to do it right.  Oooops...there went all your online savings.  C) You read correctly...tune-up the bike.  They all come out of the box needing at least minor adjustments.  D) Buying online, what sort of after-the-sale "Service Warranty" do you have?  NONE!  All bikes from a REAL bike shop come with a service warranty good for at least one FREE tune-up as the bike gets settled in.  Spoke tension on the wheels might need to be adjusted.  Or, shift & brake cable tension might need to be tweaked.  

If you truly want to "make sure" you get "the right size of hybrid/city bike" - follow these five, simple-to-understand words...  Go To A Bicycle Shop.  The $$$ stays in a local community business.  You'll get a MUCH better product.  You'll get a local warranty!              

Wheel size determines how fast you can go. For example, in the old days, the 27 inch wheel size was standard in the USA because a cyclist can go faster with bigger wheels. Mountain bikes are slower because they have 26 inch wheels. Later the US adopted the international standard of 700c wheels for road bikes, even though it is slightly smaller than 27 inches. 

Frame size is determined by how tall a person is. A person who is 5 ft tall may ride a road bike with 700c wheels if he/she can find a frame that is 48cm in size. In contrast, a person who is 5 ft. 9 in. can ride a bicycle with 700c wheels and a frame that is 54-56cm. A person who is six foot can ride a road bike with 700c wheels and a frame size of 60cm. The frame size determines how much room there is between the crotch of the bicycle rider and the ground. For example, if a person wears a pair of pants with an inseam of 31 inches, he may fit a bike that has 700c wheels and a frame size of 56cm. 

Nearly any frame size can have most tire sizes. This calculator will let you know the ideal frame geometry if you could afford to have a custom built frame made to fit your particular body build.

https://www.competitivecyclist.com/Store/catalog/f...

Therefore you should try and get a  manufactured frame that's as close as possible to what would be your ideal frame geometry. Take this knowledge and go to a reputable bicycle shop. There they can fit you and adjust the bike for you so you'll have maximum comfort while riding.