Best way from LHR to Cambridge

Train or bus (National Express, from Victoria Coach Station).

Lavandula

Best is subjective.

If you want to stick to public transportion, my suggestions are:

1) Piccadilly Line from Heathrow to Kings Cross/St. Pancras. From either of those two stations--across the street from each other--get a train to Cambridge. Use http://www.nationalrail.co.uk for train schedules.

2) National Express coach to Cambridge. No need to go to London Victoria Coach stations as there are direct coaches from Heathrow to Cambridge.

The other rail route is the Elizabeth Line to Liverpool Street, then Liverpool Street to Cambridge.
A little slower than from Kings Cross but cheaper as there are always walk up cheap Advance fares.
National Express leave at 5.15pm and 7.20pm.
The only problem with any of the three rail routes (the third is Elizabeth Line to
Farringdon then Thameslink train) is that on a Monday to Friday you will be travelling in the evening peak when the trains are very busy.
From Victoria coach station Flixbus also run to Cambridge.

In fact @Lavandula is incorrect. Since Covid National Express no longer run from Central London to Cambridge, only from Heathrow. At Heathrow they start from Terminal 5 then call at Central Bus Station for Terminals 2 and 3.

"Best" is a subjective term. Are you looking for the easiest way, the cheapest way, or the fastest way? That makes a difference. :-)

If it were me and I had luggage, had just flown in and was probably a bit sleep deprived or jetlagged, I would follow Frank II's advice and go with the National Express coach. They will store your luggage for you on board, so you don't have to worry about finding space for it, and it will get you there without having to detour (and change) through London.

It's not the cheapest way but would almost certainly be the easiest, in my opinion. And you might even be able to catch a nap while you're riding. :-)

we took the National Express Bus from LHR To Cambridge. It's a 2 hr 20 minute bus ride. The luggage is stored underneath.

Got off at Parker's Piece in Cambridge and walked across the park to our hotel, the Gonville Hotel. Stayed here two nights before moving to our University Accommodations. We'd return to the Gonville Hotel in a heart beat. If you are staying elsewhere. you'll want to get an uber or taxi from Parker's Piece to your accommodations.

Note, that when we were there several years ago. Parker's piece stop was just a stop along the sidewalk. The driver will unload the bags in storage onto the sidewalk.

As for National Express bus fares, he most expensive tickets are when you just show up and buy it then.
We pre-bought our tickets to get the cheaper price, but if you do that, buy the refundable or changeable supplement.
Its hard to time when you will get through passport control and luggage pickup and walk to the bus area, so its possible to miss your bus time, in which case the tickets are non-refundable and you'll have to pay the expensive rate. So the changeable supplement is worth the price.