T1-11 isn't a great product for siding. It's almost impossible to stop it from absorbing water and rotting away. It's big selling point is it's price and ease of installation. If you are committed to using it, then protecting it is critical.
Stain soaks in and then slowly fades away. When new, it offers decent protection at keeping moisture out, but it's a ticking clock that will require additional applications on a regular basis depending on your climate. Usually it starts to fall apart at the bottom.
Paint provides a barrier that keeps moisture out, but T1-11 is a sponge that makes it harder then most materials to get a really good paint job. Primer and caulking is critical. It will soak into the wood and provide a stronger bond for the paint. Zinsser is my favorite primer. A good quality paint makes a difference. I think Valspar Duramax is the best for the price in exterior paint, but Sherwin Williams and Kelly Moore both make excellent exterior paints for more money.
I haven't installed T1-11 in well over a decade. I tell my clients that I can't warrantee, and that it requires constant maintenance to keep it protected. Even with the best paints, it will crack and open up fairly quickly, and require additional painting to protect it. In every case, they agree to spend a little more for SMART siding, or even better, go with Hardie.
SMART is a high grade OSB that is stronger and denser then the construction grade OSB that is used on houses for sheathing. It has a solid finish that keeps moisture out and hold paint very well. It cuts and installs just like any other wood product.
Hardie is cement based, it's bug proof, fire resistant and it holds paint better then anything else. It's draw back is requiring a special blade to cut it, and it's fairly weak which leads to breaking when handling. It requires a backer of some kind when installing. Usually OSB, and house wrap, or ZIP Siding. It's more labor and money to install it, but when it's done, you never have to mess with it again.