I'm sure this topic has been discussed here before, but can someone tell me what the best type of bullet and grain weight that I should use for my Rem 742 30-06?

My father will be hunting with a Sako 270, can someone suggest the same info for this gun also.

Several manufactures make quality bullets that will work on elk, the best aren't cheap, but it's a small price to pay compared to the other equipment you will be using on an elk hunt. I'd go for something in 165gr. to 180gr. for the .06, topped with failsafe bullets, partition, or the swift A-frame bullets. Out of the .270, I'd go with the fail safe or the partition in 140gr. or 150gr. Be sure to sight in with the shells that you decide to hunt with. A 150gr bullet from one manufacturer won't necassarily hit the same spot as the next 150gr. bullet from a different manufacturer.
I've taken 7 elk with my .270, used the 150gr. partition on 6 of them, recovered every bullet, and took one large cow with the 140gr. failsafe, and did not recover that bullet as it went all the way through. The .270 is good out to about 200yrds., from there it just lacks in power on elk.GOOD LUCK!

Thanks for the info, I was a little worried that the 270 might be to light for Elk, but if you've killed that many elk with the 270 then I probably shouldn't to concerned. I am surprised that you would use a 150grn bullet, that's still big enough should I encounter a monster bull elk?

I should also say that the 150gr. noslers were also hand loaded ammo, and I took a fine 6x6 with my .270 at about 125yrds. I think my longest shot with the .270 was near 200yrds., I just try to hunt smaller meadows to limit the distance that I can shoot. The cow that I took with the fail safe was only about 50yrds., but she was quartering away and it went though the far shoulder, so I was impressed by the fail safe, which was factory ammo.I've taken alot of kidding over the years in camp about my gun, like how many pumps do I put in it etc., and just recently went up to the .300 win. mag. I haven't gotten the chance to take an elk with my new rifle in the last two years, so I can't say that it kills 'em any deader. Several guys in camp use the 30-06 with much success, one guy took a bull at near 350yrds., so it is plently of rifle in the right hands.

Try the various Federal High Energy and Hornady light magnums and pick the one that shoots most accurately out of your gun.

If you don't handload (I don't) I'd go with Federal 180gr Partitions in the 30-06.
As far as the .270 I couldn't tell you.

"Hunt smart, know your target and beyond"