Where to Find Them
If you know exactly which stamps you want or have an idea of the theme (i.e. "Desert" or "Hawaii") I'd start by searching on eBay to see what's available. This link will jump you right to the US Stamp section on eBay where you can browse by category or conduct a search. I'd recommend adding the word "sheet" to the end of your searches to avoid some of the singles and postcard listings that might come up. If you spot a specific stamp that you love, try searching by its Scott #, as many sellers will only list them by that number. Some of the more popular stamps (like the floral "LOVE" stamp used on mine - Scott #1951) will go for above face value. If you want to avoid the more popular and pricey stamps, putting together a color theme with the less in-demand stamps would be a good way to go.
Not sure where to start with your theme? Let a stamp enthusiast on Etsy do the curating for you! Below are some Etsy shops who have curated some seriously ogle-worthy stamp collections:
Little Postage House
Mail Maid Stamps
Tips & Tricks for Using Vintage Stamps
1. Know the size and weight of your invitations before you get to stamp shopping. Square envelopes will cost you an extra 21¢ per letter with less room for addressing, while heavier invitations could run you 70¢ or 89¢.
2. Have a glue stick (or several) handy! Most of these stamps have little or no adhesive, and you don't exactly want to lick 30-year-old adhesive anyway.
3. Arrange, glue, then address. Vintage stamps come in many shapes and sizes, so you'll want to decide on the arrangement that looks best and leaves the most room for addressing before you get to gluing. Once they're glued, you or your calligrapher will know exactly how much space they have to address!