See Wikipedia page on .303 British for dimensions. Best to get load data from reloading manuals, but I see the old redcoat @Kiwi Sapper has been helpful.
Note the Lee Loader system only neck sizes (does not do anything to shoulders or body of cartridge) so if the rounds were previously fired in another rifle than yours, the shoulders may have expanded too far ahead for the cases to fit in your rifle's chamber. You do need to chamber one and see if the bolt will close on it. If not closing on it, you definitely are looking at pulling the bullets and looking for new cases. That is however not something you should do unless in a safe place to also shoot it, i.e. not in an urban garage.
The step not often mentioned in instructions on how to use the lee loader is to anneal the cartridge neck BEFORE resizing the neck. Ensures it does not spring back and gives bullets a uniform grip.
Also, deburring of the edges of the cartridge mouth is important, inside chamfer can be improvised with for example a handheld 12mm drill bit, cartridge rotated a few times with very light pressure.
If you have only one rifle though, the Lee Loader is fine. When I use mine, I have a heavy, flat, iron ingot that I place on a padded stool, and use that as the base for the loader. Really cuts down the high pitched clanging hammering noise. Plastic/wood hammer (or rawhide hammer if you remember those) to avoid undue dents in the Lee Loader's steel surface.
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