#44 use 0.25 amps at 6.3 volts, so assuming you wire the lamps in parallel, you will be pulling about 15 amps from a transformer. Assuming open air wiring, you can go with 16 or 18 gauge wire. I would break down the sign lighting into smaller groups instead of all the bulbs being on one parallel circuit. Put about 15 bulbs per circuit, so you would have four or five sets of wires leaving the transformer to go to the sign.
Since you will need a transformer, make sure on the primary you use a three prong plug on a GFI circuit. If you want to fuse the primary, I would use a 1 amp fuse, too. Make sure there's a cage around the transformer - you're dealing with potentially deadly voltages, and you may have to deal with stupid.
Hope this helps, which is given without warranty or guarantees, and should be used only at your risk. I assume no liability.
Bill C