Bore diameter does not determine bullet size. groove diameter does.
Before loading you need to buy bullets. 303 bullets are 311, 312 or 313. When any of those get hit in the ass with 50,000 psi, they will fit the barrel.
A flat base bullet will probably work best. I suggest you start with 180 gr. I would buy a box of round nose and a box of spitzers. I would load 34 to 38 gr of 4895. One of those should shoot well.
If you want to slug the barrel, get a unsized cast bullet. This will be 313 to 315. Clean the barrel well and leave a light oil in it. I start the bullet at the muzzle, where I can start it with a hammer. Once it is in the barrel, the engraving is done. You can either then use a cleaning rod to tap it all the way through to the chamber, or just tap it back out. measure across the bullet to get groove diameter.
If you can locate a suitable size soft lead ball, that would be easier to push through the barrel than a hard lead bullet.
personally, when I want to slug a barrel i load an unsized lead bullet over 6 gr of RedDot and shoot it into some water.