Id suggest reading lymans cast bullet handbook.
Get a book, better yet, get several and do some reading and studying. Getting answers to specific questions from the internet is useful, but a good book has benefits the Internet can't provide.
Lyman has been making reloading and casting tools & molds since the late 1800s. NOBODY has a greater institutional experience.
I would like both to have good trajectory, weight and hardness while still getting a decent penetration and mushrooming.
Be aware that it may not be possible to get everything you want, in the degree you want.
Casting bullets isn't rocket science, but its not "plug and play" simple, either. There are LOTS of variables, and they need to be addressed in the correct way to get acceptable results.
The alloy used determines the velocity range suitable. The specific proportions of lead, tin, & antimony commonly used give both good performance in shooting and in casting over a broad range of uses.
Bullet to barrel FIT is another critical factor. A proper alloy, incorrectly sized will lead the bore as badly as an improper alloy (at the given speed)
Generally lead bullets should be approximately .002" over groove diameter for best results, but this can vary a bit.
Every gun & bullet combination is a unique individual in the way it behaves. Things tend to follow general trends, but exceptions happen, often.
Mushrooming, while getting the other performance you want is often the most difficult thing. Soft enough to mushroom, but hard enough to go fast is not an easy trick to pull off.
Most of us accept that, and choose velocity (and penetration) over mushrooming ability, if we have to choose. Hard cast slugs seldom mushroom, some don't expand at all. Expansion is nice, when you can get it, but don't give up other performance to get it.
You'll definitely have to use a gas check on the .30-06,
No, you don't have to, but at higher speeds you will want to.