Inherited Approximately 120,000 Pennies That My Father

ok like WOW! - that is a lot..

Here is the algorithm (pay close attention

1. Do you still work?
1a. If yes, take them to the bank for $1200.00 because the odds you will get $2000 without investing a huge amount of time are extraordinarily low.
1b. If no go to step 2.

2. Are you bored?
2a. If no, see 1a.
2b. If yes, go to step 3.

3. Are you married and prefer to stay married?
3a. If yes, see 1a.
3b. If no (to either premise) go to step 4.

4. Do you have at least 4 months to devote to this?
4a. If no, see 1a.
4b. If yes, see the post by Pacificoin and get started.
You should be able to process, say, 5 coins a minute after the first 1,000 coins. That's 1200 in a 4 hour work day, which gets you through them all in 5 to 6 months working Mon-Fri.

Furthermore ...
Since I was already pulling coins out of pocket change shortly after 1962, I can assure you there will be very few Indian Heads, and the ones you will find are likely to be common dates worth only a couple of bucks.
And, if your dad lived on the east coast, there will be very few D and S mint Lincolns in this trove.

Who are you and what have you done to the Frog (fka King of the Cynics)?

Just me... I'd dig through them and spend a little time separating wheats from everything else. If other pieces show up, set them aside as well. For memorial cents, I'd look closely at the usual suspects--1995, 1969 S, 1972, etc. Do the same for noteworthy wheats (too many to list here). Also, wheats could yield some striking examples of die cracks and laminations--just the dramatic stuff, not minor examples. Again, only speaking for me, I could accomplish a decent 'high level' inspection of 120K cents in about six hours spread over a few days. No way would I spend 12 seconds on each and every piece.

Yes, it's only a half ton after all

I guess that's what bathtubs are for.

This is a once in a lifetime opportunity. Unfortunately if you don't like sorting through coins it might seem like it would take a lifetime.

If you can't face the prospect of doing it yourself, perhaps you could enlist a local coin club if you let someone have a piece of the action.

Definitely sort by year and mintmark, and get that book that was mentioned. Also look for minting errors like clips and die cracks.

When looking for varieties it is best to look at one year and mint mark at a time. For those years and mint marks that have no varieties they can simply be returned to the bank.

IMO, if you are not interested, committed, or needing to maximize the monetary value of the hoard, a worthwhile option is to blindly roll with the aid of a Nadex coin manager and be done with it. You would be surprised at how many rolls you can do while watching TV and who knows, something may catch your eye in the process. Then dump them at the bank in multiple lots and give someone else a chance to find what they are looking for.

Bottom line is you have to decide if your time and interest is worth $1200 or spending a lot of time to potentially finding some 'jewels'. Maybe start with a pile of a 200 hundred/4 rolls and see how that goes to get a feel. Cross check against Numismedia and see what the values are and go from there. It won't take you long to figure out if this is your thing or not.

Remember, you don't eat an elephant all at one time, you take small bites and many meals.