Flight arrival time vs Airport departure time

Immigration security first. Could be long lineup; could be stroll. Then customs. If nothing to declare, walk through green door. Maybe spot check, not likely. Not hassles; routine of travelling anywhere. ATM machines possible inside secure areas or in lobby which will be crowded more or less. Gatwick probably Travelex rather than a bank machine but since time matters to you just grit teeth and pay slightly more.
Modern airports typically maintain extensive websites with lots of information to help you navigate. Google any of those three to reassure yourself that all will be well. Print out maps or load onto smart device.

In order to know what you will encounter on arrival at each airport, we need to know which airport you are arriving from.

For instance, if you are arriving in Munich from Gothenberg, both are Schengen, so there will be no immigration (passport control). Both are EU, so there will be no customs (goods control). It will be similar to a domestic US flight - you just follow signs to "ground transportation" and exit the airport. But, if you're arriving in Munich from Moscow, you will need to go through immigration and customs.

Customs in Europe is usually just a matter of walking through the Green Channel Nothing To Declare line. Unless you're "randomly selected for additional screening" (possible but rare), you're done.

Time spend in immigration lines cannot be predicted. It all depends on how many other flights arrive at the same time, and how many agents are on duty. If you are indeed flying US to London, London to Gothenburg, and Gothenburg to Munich, you will only go through immigration on arrival at London. you will go through immigration on arrival in London and in Gothenburg. From Gothenburg to Munich, you will not go through immigration, since both are in the Schengen zone.

If you are flying from Munich back to the US, you will go through passport control on exiting Munich (this is usually faster than immigration on arrival).

EDITED to reflect Frank II's (accurate) correction.

One correction to the above....if you are flying London-Gothenburg-Munich, you will go through immigration in both London and Gothenburg. (London is not part of Schengen and Gothenburg is your entry into Schengen.)

Unless you have something to declare, you can walk through the green customs doors in London and Gothenburg and the blue door in Munich (if there is one.) If not, green.

As stated, on arrival you first go through immigration/passport control, then through baggage claim to customs. Walk through customs and then you are in the terminal.

You probably won't have any hassles as long as you are just there for vacation.

You'll find ATM machines all over but some ticket machines will take credit cards.

If you are not flying in that order, please let us know from where you will be flying and we can tell you what to expect.

Airports don't just have websites, they also have their own official apps, and there are 3rd party apps to guide you through airports, too. And the apps of the major airlines, like Lufthansa's, also are helpful to find various offices and services inside the terminals.

Try also youtube searches for helpful clips of people doing walk-throughs of the relevant places so you can see exactly what's there.

In order to know what you will encounter on arrival at each airport,
we need to know which airport you are arriving from.

1. Orlando, Florida to London, England
2. London, England to Gothenburg, Sweden
3. Stockholm, Sweden to Munich, Germany
4. Paris, France to Orlando, Florida

Orlando, Florida to London, England

You will have immigration on arrival in London, then customs (as I said above, just a walk through). These immigration lines are often long; expect it to take an hour. Be pleasantly surprised if it's faster, and don't be too upset if it takes longer (if you have young kids, prepare them).

London, England to Gothenburg, Sweden

Frank II is correct. You will have immigration on arrival in Gothenburg (going from non-Schengen to Schengen), but no customs (both are EU). Be aware that London has six airports, at least as far as the airlines are concerned; make sure you go to the right one!

Stockholm, Sweden to Munich, Germany

No immigration (both are in Schengen) or customs (both are EU). Similar to a domestic flight in the US; when the plane lands, you just make your way out of the airport with no "formalities."

Paris, France to Orlando, Florida

You will have passport control on leaving Paris, as it's your exit from the Schengen zone. You will not deal with customs in Paris unless you are trying to get refunds for VAT (if you want to do this, allow extra time). On arrival in Orlando, you will go through immigration, then pick up any checked luggage, then go through customs (not a walk through; an agent looks at your form and may ask you questions, or may just stamp the form). Again, how long immigration and customs will take in Orlando is hard to predict.

Airport ATM's are usually well signed, but if you're feeling unsure, do go the official site for each airport to see where they are.

Thanks Harold. This info is now saved in my itinerary.

I just want to add on to Harold's excellent answer.

When walking through customs in London, there will be two exits--one green, one red. Unless you have something to declare, take the green one.

In Gothenburg and Munich you will probably see one that is blue. It will say "EU arrivals." Again, if you have nothing to declare, take that one.