For moose, most people choose a 174 to 180 grain bullet. (There is one brand-new exception to that rule, which I will suggest below.) If you go with the 174-grain Hornady roundnose, you can't go wrong, but your range will be limited to a maximum (under ideal circumstances) of about 200 metres. Probably 100 yards is a reasonable maximum for guaranteed performance and accuracy out of an old Lee Enfield. Some rifles will clearly do better, but most will agree that with this load and an old barrel, your maximum ideal range will be somewhere between 100 and 200 yards.
Personally, I really like IMR 4320 in the .303 and that's what I use. Others swear by powders like IMR 3031 (a classic choice that goes back to WWI), IMR 4895, Reloder 15, Varget, H414, and a host of others. From personal experience, I like IMR 4320.
My rifle has shot well with the 174 Hornady and 42 grains of IMR 4320. Your rifle may not like this combination, and obviously, you should work up from well below. You just don't have as much margin of error in older military rifles, and it pays to proceed cautiously. The Hornady bullet is capable of excellent accuracy, though, and it supposedly expands and penetrates beautifully at .303 velocities.
The more modern choice I referred to above will likely become my personal favourite, if I find that it works in my rifle. I'm speaking of the brand-new 150-grain Barnes Tripleshock that's been announced for 2008. This is the first major premium bullet that has been released in the .303 caliber in North America, and it should be awesome on any game from deer through moose. Iit should easily work out past 250 yards (even 300 yards, depending upon the accuracy of your rifle). I wouldn't hesitate to use a solid copper bullet like this on moose, even if it only weighs 150 grains.
So far, most .303s of my acquaintance like something between 45 to 46 grains of IMR 4320 with a 150-grain Hornady bullet. This is more than maximum in the book.
I plan to work up a load with those new Barnes bullets once I get my hands on a box. I will be using IMR 4320 and working up to the load that gives the best accuracy, never going beyond 46 grains, however.
I'm sure others will chime in with their choices and experiences.