I used to design and print stationery in SF, and I worked with customers who wanted to DIY as well, so I can give you some general info.
Designing: If you have a PC, you can design your invites in Adobe Illustrator, Microsoft Word, or even Power Point. If you want specialized invite printing software, Printing Press by Mountain Cow is a really easy program, and even has a built in envelope addressing system. The program’s between $30 and $100 depending on the version. If you have a Mac, you can design in Illustrator or Pages (smiliar to MS word, but easier, haha). You can buy images or design motifs through websites like Veer.com, which charge a fee for the use of the image. The fee is variable from a few dollars to $50+. Or you can use CD-Rom books like those from Dover Publications, which have themese like Ornate Frames, Birds, Decorative Ornaments, etc. These CD-Rom book sets usually run around $20, they’re copyright free, and have hundreds of images per book. You can also buy fonts from $20-$100+ from veer.com and myfonts.com. Free fonts are available from dafont.com and fontsquirrel.com
Printing: Ink Jet printing will probably be your easiest for at home printing. I love Canon Pixma’s, which run from $75-$300, depending on the model. The colors are crisp, the inks are sold individually, and cardstock and envelopes can be fed through easily. The only downside is that you can’t print on metallic papers. If you want to print on metallic stock, you have to use a laser printer or have your work professionally printed. Laser printers for home use are expensive, at least $400+, and can get much pricier if you wanting a Color Laser. You can have your work professionally printed by a local printer, usually by a flat printing method, but this will be more than printing at home, obviously, and you may be limited in what type of paper they will print on.
Paper: My favorite resource for paper and envelopes is http://www.envelopperinc.com I like them because they have paper, cardstock, pockets, inner and outer envelopes, folders, tags, place cards, belly bands, folded cards… basically anything you can think of, all available in their full range of colors. They have favor boxes and tagss, and have customization options, too, like hole punching, scoring, and custom cutting. I especially like their euro style envelope flap, and the fact that you can get free shipping. There’re a few other sites for paper, too, like cardsandpockets.com envelopemall.com but I haven’t been as pleased with their products.
Please let me know if you specific questions, as I’m always happy to share what I know. Good luck to you!