cudatruck,
welcome to both addictions (handi's and 45 caliber rifles)
The thing about the 45-70 Handi is it has many personalities. So bullet choice depends on your intended target. Pigs and Bears something in the 400 grain range running 1,800 fps. Deer, there are differing opinions here, but I did not like the performance of the 400 grain hard cast bullets on deer (two) that I tried it on. So I am trying 300 grain hollow points this year, 350 grain bullets also come highly recommended. 500 and 525 grain bullets are used for 1,000 yard target shooting by those who shoot much better than I do with open sights.
My go to powders for all non-magnum rifles are IMR 3031, and IMR 4064. In most cases these give good velocity (not top velocities), fill the cases at least 80%, and make accidental overloads or over pressure loads difficult to achieve without trying.
Have fun, experiment (or play) with it, and read up on the history of the .45-70. Both Elmer Keith, and Paul Matthews hold the .45-70 in high regard in their writings. 53 grains of 3031 is a load both mention often.