The existing wiring (2003 Mustang) is designed to be used with #9007 bulbs which are rated for 65/55 watts.
If you get H4's that do not exceed this wattage rating, you should not have a problem. But some H4's (the ones that are not street legal) are rated as high as 100 watts - for these I would use additional relays, and heavier wiring just to be safe.
Sealed beam 7" halogens are also rated for 65 watts, so they should work with the Mustang wiring without any alterations. Of course, in 1951, the headlights would have been 6 volt, so you would have to replace them with 12v sealed beams if they're not already.
I never wire headlights with anything less than 16 gauge, I usually use 14, but that's just me.
If you get the headlight conversion kits, just do exactly what the instructions say and you should be fine.
Hope this helps...