If you have a contactless card or an Oyster card, quickest is the Tube (Underground), runs about 8 times an hour. Travel between Heathrow terminals is free on the tube, but you need an Oyster or contactless card so they can make sure you only went on a free trip! Otherwise take the free connection on the Heathrow Express train, free, but 4 an hour. Either way journey time is about 5 minutes, plus waiting time for the next service.

BA bag drop closes 45 minutes before departure, strictly enforced (as is entering the security queue by 35 minutes).

I'd say you need to leave an hour from scheduled arrival until you can expect to be clear of immigration and baggage check. (Customs is easy, you normally walk through without speaking to anyone or stopping). Allow 10 minutes walk to tube/train, then wait, then travel, then 5 minutes up to the BA desks.

Beyond that, it depends on your taste for risk, and what your travel insurance covers in the way of missed connections. BA are unlikely to be all that helpful if you rock up late saying "United delayed me on a totally different ticket". Delays at Heathrow are fairly common, as the airport operates basically at capacity. Depends on your risk tolerance, and what your travel insurance will cover!