Plan on loaded touring next year. I have a Schwinn Paramount steel frame that has been modified for touring. I will be using 700c x 28 wheels. I intend to replace the double crankset with a mountain bike triple. My question, should I install a 22-32-44 or a 26-36-48? My cassette is an 11-32 that I plan to change to 11-34. I have Shimano Deore XT M732 derailleurs.

you can always buy a few different, larger outer chainrings ,
with the 22 as your low, say a 46~8, 34~6

110 74 , 24t is as low as you can go. 34 for the larger set.

I put in years of touring on a 7 speed 14-34t freewheesl, and a 50/40/ 24 crankset.

with the 11 and 12 t top cogs you don't need big gears
44:11 and 48:12 are both 4:1 ratios.

go 22/34/44 up until 2 days ago I was gonna go 48/36/26 but then i ran sheldon browns gear calculator and saw that a 42/11 gear still cranks out 30mph at 100rpm ( i have a high cadence) thats plenty fast and going down hills you will go much faster than that just coasting. Your main concern should be getting up big hills loaded up.

Go with the smaller chainring combo for the reasons motobecane69 mentioned. And consider a 9 cog cassette for the smaller jumps.

Here's a link to Sheldon's Gear Calculator. Great tool, especially when set to calculate mph at a given spin rate. I've found the 22/34 combo to be iffy for long, steep climbs simply because I can't spin fast enough long enough to keep the bike moving in a straight line. You probably can.

With a 110/74 BCD I would go with a 24,34,46t chainring and run a 11-32 cassette.I have this setup on my LHT and love it.And I am building a Big Dummy with the same setup.It works good for me.With time you will learn what is best for you.One of my bicycle is a Nashbar touring bike and I run it with 700cx28 and it rides great its fast as heck I think very light weight.I love building bicycles you get to pick what you want to go on it. :-)
Oh by the way you can order the crank arms and build your on crank set like I did it will cost you a little more this way but I like it better just me.

I'm relatively fit and use a 26/38/48 crank with an 11-28 cassette for "credit card" tours. For me that means around 15-20lbs of stuff (camera, phone, cool weather gear, change of clothes, spare parts, mini U-lock, etc). The 26/38/48 makes multiple steep climbs per day possible, if not easy. For loaded touring, where I would expect gear weight to double or triple, I wouldn't consider anything other than a 22/32/44 crank and an 11-32 or 11-34 cassette. Even on a relatively flat tour, the lower gearing can be an asset (ex: riding into headwinds).

I'd suggest the 22t up front is the way to go. Lower is better for me on tour