What are the best websites where I can order old, vintage, or
collectible beads from around the world as well as suppies for
stringing and containing them?

Hi! Thanks for the question.

I have found the following online stores which sells the beads that
you are looking for.

We-R-Beads
http://www.we-r-beads.com/Merchant2/merchant.mv 

Bead Room
http://www.beadroom.com/ 

The Beadin’ Path
http://www.beadinpath.com/vintagebeads.htm

RibbonSmyth
http://www.ribbonsmyth.com/
http://www.ribbonsmyth.com/beads.htm (beads gallery)
http://www.ribbonsmyth.com/vintagebeads.htm (vintage beads gallery)

Pudgy Beads
http://www.pudgybeads.com/

Bridey’s Beads
http://www.brideys.com/beads.htm

Jewelex
http://www.jewelex.com/vbseed-1.html
http://www.jewelex.com/google.html

Tradewell Vintage Values
http://pages.tias.com/4/InventoryPage/33378/1.html

Empyrean Beads
http://www.empyreanbeads.com/intro.html 

Whole Bead
http://www.wholebead.com/blueheron/blueheron.html 

Sue’s Jewels
http://www.spilot.com/

Beadella
http://www.beadella.com/

West Artisans
http://www.wesstartisans.com/JillAverill.php3

Cliptomania
http://cliptomania.com/vintagebeads.html

Patrice
http://pmegio.com/index.html
http://pmegio.com/new_projects/planet.html (vintage bead necklace)

Bumble Bead (Vintage Beads)
http://www.bumblebeads.com/vinfeature.htm

Send Beads
http://sendbeads.com/vintageglass.asp 

Earthly Adornments
http://www.earthlyadornments.com/beadcont.htm

Harman Beads
http://www.harmanbeads.com/vintage.html 

Vintage Styles
http://www.vintagestyles.com/index.html 

Embellishments
http://www.embellishmentsinc.com/products.php3?category=B:ANT 

Dreamweaver Beads
http://www.dreamweaverbeads.com/vintage.htm 

Katie Gates Designs
http://www.katiegatesdesigns.com/bracelet.htm 

-------------------
The following set of online stores also sells the kits and accessories
you require.

Imagine Beads
http://www.imaginebeads.com/ 
http://www.imaginebeads.com/catalog.php?action=110&cat_id=49
(accessories)

Thaigem 
http://www.thaigem.com/bead_shop.php?engine=google 

Bruce Frank Antique and Vintage Beads  
http://brucefrankbeads.com/

Beads by Mail 
http://beadsbymail.com/
http://beadsbymail.com/mixers.htm (accessories & kits)

Glass Garden Beads  
http://www.glassgardenbeads.com/index.html 

Firewood Beads  
http://www.fireweedbeads.com/

Glass Cat Beads  
http://www.glasscatbeads.com/ 

-----------------------
You could also get vintage beads from online auctions.

Ebay’s Vintage Beads Auction Page
http://search.ebay.com/search/search.dll?query=vintage+beads&newu=1 

Just Beads (An All Beads Auction Site) (They also have supplies)
http://www.justbeads.com/

Yahoo Bead Auctions
http://list.auctions.shopping.yahoo.com/23024-category-leaf.html 

------------------------
The following websites may be of interest or assistance to you since
it provides bead buying guides.

Vintage Beads
http://www.midwestbeads.com/beadology/Vintage_Beads/vintage_beads.html

Beadwork at About.com (A very rich resource for everything about
Beads!)
http://beadwork.about.com/cs/beadsspecialty/

Beadwrangler's Guide to Beads & Beading Techniques
http://www.beadwrangler.com/beadguide.htm

Search terms used: 
Vintage beads stores auctions guides

I hope these links would help you in your search. Before rating this
answer, please ask for a clarification if you have a question or if
you would need further information. Thanks for visiting us at Google
Answers and enjoy your collection!

Regards,
Easterangel-ga

Thank you for all those web sites. It should keep me busy for a while.