Just to clarify terminology - Hoppa (full name Hotel Hoppa) is a bus. At Heathrow hotels aren't allowed to put on their own shuttle buses as there's so many hotels and only limited space, so there's some buses that run between the terminals and groups of hotels. They follow set timetables. I'm not a big fan of them as I think they're overpriced for what you're getting.

The trains from Paddington take you directly into the airport, for T2&3 there's moving walkways from the station to the terminal and in T5 you just take a single lift from platform level that takes you straight to departures level. If you're going between terminals on the train these are just the regular trains they just happen to be free between the terminals. Therefore to go from T4 to T5 you need to change at T2&3 (which is why I prefer the bus between T4 and T5, neither is ideal for luggage).

In your case with a lot of luggage I think it's probably worth paying for the Hoppa if you're staying in Hilton T4, less walking and unlike the free bus there's sufficient luggage space. If the newly opened HGI T2 is available then the free train between terminals would be the best option (I'm guessing, as it's not opened yet I can't comment on the walk between the hotel and the station).

For the HGI Hatton Cross it depends how much luggage you have, it's very close to the tube station but you need to cross a busy road (there's an option of both a footbridge of traffic light controlled crossing so it's safe).

Perhaps after saying all this as a first timer it might just be worth taking the option that seems the least hassle as long as you're happy with the price.