2003 Honda VTX 1300 starts fine but stalls when you shift into 1st

You should change spark plugs. If you you have after market pipes you need to have it rejeted or the problem will continue.

Let me see, 1 down = 1st gear, 1 up = 2nd gear, 2 up = 3rd gear, 3 up = 4th gear, 4 up = 5th gear.
See, easy.

if you are able to select gears without the motor stalling I doubt that your clutch is burned I would suspect that you may have sheared the output shaft in the gearbox this is a major job & without the correct tools & knowledge should be entrusted to a qualified technician

Make sure the choke is pushed ALL the way in. If you've been using it, you may have fouled the plugs.

ever drain your carbs ? should be done seasonally . fuel filter problem, sounds like it is running out of gas.

The pick-up coil next to the stator could be bad as well.

You should check your side stand switch, this will kill the motor