while the OP is not gonna come back in to update his build i thought maybe he would like a couple nuggets of info.
keep in mind im not saying how you should build your gun - as that seems to be a trigger for you - im just gonna share with you a couple things ive personally experienced with 10/22's and building them.
1) i received my first 10/22 as a Christmas present when i was 10 or 11, bone stock because back in the 80's there was no such thing as upgrades.
i have over 100,000 rounds down that rifle and i still have it!
when i get my son his first my plan is to do the same thing, just give him a bone stock one.
once he gets comfortable with it and starts to figure out what he does and does not like then ill start to upgrade and swap out stuff.
2) when your building a 10/22 usually you build them with a purpose in mind. i say this because i have 12 of them and each of them i build or tweaked specifically for something. be is bench gun, gopher gun, pack gun ect ect.
3) building a 10/22 is expensive! while i too would like to build my son a $1500 10/22 for his first gun thats like me giving him a turbo'd mustang for his 16th birthday instead of a 2007 Dodge Caliber.
anyways back to your original question.
barrel length and keeping it legal.
to determine what you need for a barrel length you need to first decide on what you are going to use for a stock as you need to hit that 26" mark.
you could in theory have a 20" stock and a 6" barrel if you wanted.
i know i have a Boyd blaster stock and a dlask 8.5" barrel and its just a hair over the minimum.
TacSol makes a uber light barrel, married with the Hogue stock the entire gun is light as a feather.
nothing wrong with a stock one, this is mine from 1984, the stock barrel is nice and light.
could always go cheap cheap and look for a RIA knock off and pick up a ruger stock off EE, they are not very accurate guns but they are fun!
bench gun, heavy!
there are always special edition 10/22's that are out, like this 50th Anv contest winner, couple tweaks like a Brimstone strigger group and its a beauty.
you could go mid 90's and flesh out a Butler Creek folder
dont discount the 8.5" Dlask barrel if you want a light barrel, its so short you dont notice the weight of it being a bull barrel.
i do believe Dlask also makes fluted barrels now as well, which would cut down on weight.
a real nice build is a Dlask 10.5 or 12 on a stock ruger 10/22.
my co worker has that, real nice and simple and cheap to get into.
pick up a Ruger BX Trigger and your good to go.
look at stock replacement or refinishing later - good dad and son project.