for me, any flight under 5000 miles is doable in coach provided I am seated in an exit row or bulkhead seat. For longer flights, the most you'll need is Business class, or even Premium Economy is acceptable (not UA's E+). The thing is, coach is cramped, you have no lateral space and no vertical space (pitch). You're stuck in one position for a long time. Even premium economy gives you more space in front and side to side. That makes a huge difference. Lie-flat seats are just gravy, you can easily sleep in cradle style seats.
The best way to sit in business cheaply is to use miles. Don't waste your miles on economy.

First class is nice, I've sat there before, it's generally easier to get a seat in First with miles than in Business. First gives you some extra amenities over business, like access to the First Class Lounge, first class checkin, even earlier boarding, slightly wider seat, a 1-2-1 config that gives everyone aisle access, smaller cabin, slightly nicer meals, slightly more attention from the FAs, etc.

My analogy:
Economy Class is like being confined to a Texas death row prison cell.
Premium Economy Class is like staying in a motel 6 room.
Business Class is like staying in an embassy suites hotel room.
First Class is like staying in the royal suites of the Intercontinental hotel.