I know this sounds a stupid question but i'm not sure if you continue to turn up in civvies or do you need to pass phase 1 or something before you can wear it or do you just wear the stuff immediatley.
My fathers WW2 battle dress is still in the attic. However, since you have been issued with a uniform, but have not formally passed muster as a TA soldier, I would recommend that you wear those bits that you are comfortable with for the time being. The rest can be worn later when you are taught such things as how to tie shoe laces and how to button a shirt up correctly.
What F***king standard are they letting in to the armed forces , when we have questions asked like that , no wonder the TA is slated and god help us if this is the part of the five thousand to replace regs.
If I were you I'd wear your uniform to your civvie job too. And around the house. In fact, go to sleep in your issued sleeping bag wearing nothing but a headover & an S10 - you'll soon feel like a soldier.