Stores sometimes sell products similar in price to thrift store finds. When is comes to a basic tee, Forever 21 is definitely my first stop. They have great variety and an awesome selection for cheap.
I know the hoards of clothes and the bright neon leggings blinding you from the rack can be overwhelming, but just push through to the section you know you want and you'll be fine.
Also, I think if you want to achieve a more professional look, it is all about the quality of the materials you use. While the lace was some leftover pieces from my sister's wedding dress and was free for me, it originally was an expensive high-quality product. Because you are using such a small amount of fabric for a project like this, think outside of the box for your material and try to find remnant pieces that have been highly discounted, but aren't cheap products and you will be more happy with the end result.
As a side note, make sure you place a piece of paper or something similar underneath the front of your shirt for any excess glue that leaks through. You don't want to be gluing your shirt together.
My husband thinks lace equals Granny. I definitely disagree with him on this one!