Sorry other posters, but I beg to differ. Having a separate border does not always look like an kindergarten art project if it's done properly and quality materials are used. My invitations were done this way & I was told by many people that they were the most beautiful wedding invitations they had ever seen. That being said, I didn't do it myself, I paid an artist to do them. I thought maybe you would like to look over her gallery for ideas on how to do it right... scroll down the page to see lots of projects; most with glued borders! http://www.momentaldesigns.com/wet-paint/
Look through her whole site; she has many beautiful designs and ideas. I used her tree invite. The leaves and flower petals were my wedding colors, green & plum. One of the things that make her invites stand out is that she uses metallics to hand-paint the little details and you choose border colors that match to make it "pop". I went with a double border of chartreuse and plum and had her add a leaf here or there in metallic copper (fall wedding). They were amazing!
As far as glue type, I can't tell you what to use, but get some extra card stock and practice gluing them together so you use the right type of glue. You want to make sure it doesn't stain through the stock or chunk up and leave a bump. And make sure it is strong enough to hold together after they're mailed. Read this board I found for a discussion on the best adhesive for card stock...
http://boards.weddingbee.com/topic/best-adhesive-for-stardust-paper
For envelopes get the ones that are the same size as a half-sheet of paper (8.5 x 5.5). Make your largest border slightly smaller, then make each piece to be glued on top about 1/4 to a 1/2 inch smaller depending on how much border you want to show. You can probably get a good paper cutter and cut everything yourself. Keep in mind that I paid $7 a piece (a splurge on my budget but I only needed 50). You can get a high-end look for a lot less money if you makes these yourself.
If you are artistic and enjoy projects like this, then don't listen to the other posters. In the end, you will end up with something beautiful that is totally different than what can be purchased. Yes, some people don't think it is worth spending so much time on such a small part of the big picture, but half of the fun of wedding planning is working on the details. Concentrate on hand-doing the parts of your wedding that make you happy and hire professionals to work on the parts that don't... good luck!