Hi Jim,
It is best to have gas shielding on the back side of the two pieces you're welding together. As soon as the metal reaches 800 degrees(some say 500) the metal will start to be contaminated from the oxygen in the air. On straight pieces you can use a brass backing bar clamped in the corner to cut down on the air reaching the back side of the weld... but this is taking a chance that the metal will not become contaminated.
The best way is to make "purge blocks" and they are worth the time and trouble, to make sure the weld is 100%!
They don't need to be anything special... I've made them from aluminum foil with a tube running to it to purge the back side of the weld area. All you'll need is to "Y" the hose after it leaves the flow meter on the regulator and use a small valve to control the amount of argon to the "purge block" using a common hose. You can get the "Y" from the welding supply... everything else from Lowes or any hardware store
You will find some very good info here...
Welding Titanium
You can use cut 1/16"-3/32"strips from the edge of sheets... this is called "Poor Mans Filler Rods".
You DO NOT want to buy Grade 5 filler rod from a welding supply for a small project!!... they're so cheap!!

You can find tig rod on eBay sold by the rod... I would say around 6 or 8 rods (18" long) would do.
Just make sure you make a model from paper or other material before cutting your titanium!
All edges must be very clean before welding and your filler rod too. But this is standard with any metal and using a purge gas on the back side of stainless and other metals is common too.
We hope to be walking the beach at St. Simons Island, GA during the Thanksgiving week. Just a few miles south is a location called Kings Bay. Wouldn't it be great if places like that in the World were only needed as a fishing village?
Best at ya!
-Wayne