2 things.
1. Use copper wire. It's super cheap, and it's fine in your tun. HD caries a 14 (I think) gauge wire that you can use. It's got a green sheathing and is sold by the metre. It's used when running power through conduit. Cheaper than 14/2, I guess. That's what I used to make my braid.
2. There's no need to use the T. Since you're using a braid, you're going to have to batch sparge. All you really need is about 6-8" of that braid to do the job. Anything longer is just going to get in the way when you stir your mash. Mine is about 10", I think.
3. If you got the normal sink/toilet water supply line (and make sure it's stainless, not the plastic that looks like stainless), you don't even need the wire for support. I used one like that for a couple years with no issue. If you use the 3/4" hot water supply line, I'd get the wire for the braid.
Hope that helps.