In PHL you can access the Envoy Lounge (entry near gate A15) regardless of whether you get the upgrade as you're a Star Gold on an international ticket. When you go up, there's a club and the Envoy Lounge. Just go to the lounge, where they'll verify your access and can also help with seat assignments, upgrades (if still uncleared), etc. You can access the US club at DCA on your initial leg as well, and if you get the upgrade you can use the arrivals lounge at LGW.

Immigration in LGW is pretty easy, and so long as you walk slightly faster than the masses, lines shouldn't be too bad (at least in the past I've had good luck). It is a bit of a hike from where the US planes usually arrive, but nothing terrible. US citizens can stay in the UK for 6 months without anything other than a valid US passport for either work or vacation, so immigration is generally a breeze, with just basic questions as to why you're there. Do be honest. You'll also have to fill out a card near the end of the flight with your passport number, hotel address or other UK contact info, etc, so have this and a pen handy.

I've only had easier immigration in FRA, where they have yet to even speak to me when I give them my passport, they usually just scan it and stamp it and look for the next person in line. It's very unlikely that you'll have anything to declare for UK customs at LGW unless you're bringing something unusual or large amounts of gifts. Overall the UK is an extremely easy place for Americans to visit, with the biggest obstacle often being driving, should you need to do that. If not, take the Gatwick Express train to London Victoria and connect to the London Underground which will get you within walking distance of almost anywhere in central London. A slightly cheaper but longer alternative is a commuter train to Blackfriars, but you should avoid this if you have big luggage. I know you're arriving on a Sunday morning, but if you return during a weekday, when the trains are more crowded, the commuters don't have much patience for big bags taking up space.

On the return you can use the club at LGW regardless of upgrade status as well as one of the PHL clubs on your connection to DCA (I believe the Envoy lounge is departing only).