Which Rim Size will Fit My MTB?

1. Just replacing the groupset is not enough. 9 speed cassette has different spacing from 6 speed, so the derailleur steps won't match the cogs. For 9 speed cassette, you'll need a new hub, and the new hub is wider than 6 speed so you need to spread the frame too.

2. There are many different 26" sizes, none of which actually measures 26". For 26 x decimal inches, the correct one is 559mm

3. See above and What is the maximum or minimum tire width I can fit on my bicycle

Normally a bike frame is designed for a specific wheel size and it's not really usual to change that size unless you go for a very specific intent.

If your frame has only v-brake or cantilever brake mounts (two types of brake that squeeze the rim in order to slow down) you must stick to the same rim diameter.

If your frame has disc brake mounts, you can fit other rim diameter, however, there may be other limiting factors, for example tire clearance or toe overlap if you get a bigger combo of rims and tyres, and pedal clearance if the new combination is smaller.

Regarding tire width, most "regular" width MTB rims will allow anything ranging from 1.5 inch to 2.3 inch tire width, so unless your rims are wider than normal, you can easily fit a 1.5 tire.

I have done such thing myself: used a hardtail MTB for commuting and riding on the road by mounting 26 x 1.5 slick tires to it. (The same rims I normally use with 26x2.2 knobby tires)

Small width tires have a smaller outer diameter, so a 27.5 rim with a narrow tire may be similar to a 26 rim with a very wide tire, but it's more common to use a 27.5 tire with a very wide tire (near 3 inch) to achieve a similar outer diameter to a 29 inch wheel. (this is called "plus tire") Always consider that for this to work the frame must be designed for that or have the necessary clearance.

In my case, I currently have a frame that is designed for 26 inch wheels but has a lot of clearance, which, after many measurements and research, I determined it would accept a 29 rim with a very narrow tire (I used a 700c x 38 mm, 700c and 29 inch rims have the same bead seat diameter, that is, the same ETRTO size.).

This only worked because the frame has disc brake mounts and I swapped the suspension fork for a rigid one (the original one would not fit the 700c x 38 tire) I did this to have a hybrid commuter. The diameter increase from a 26x1.5 tire to a 700x38 made me gain about an inch of pedal to ground clearance.

For your case, I'd recommend sticking to 26 rims in regular width. You will be able to use 26x1.5 but you can also get wider tires that are slick (good for pavement) or have very little knobs which are a good compromise if your routes include dirt paths and sandy or muddy terrain.