exit fee

We always try to avoid Heathrow when possible. A major pain to travel through. Schiphol (Amsterdam) is so much better. Never flew through scotland.

I've never flown through Scotland, either. I have flown through Heathrow & Amsterdam. Amsterdam is a great place to change flights. Heathrow is a lousy place to change flights (IMO).

BUT we flew out of Heathrow a few weeks ago and enjoyed the experience to the point where I'd say it's an even toss between AMS and LHR as a departure airport.

There is no desk on your way to leave where you have to pay someone an exit fee in Edinburgh. If there is it is probably in the ticket price. Edinburgh and Amsterdam would be better to leave from than Heathrow from my own experience.
Both airports are super easy to get to on public transportation

No airports in Scotland have a fee which you are charged on exit.
The UK, along with many other countries, charges a tax on all departing flights. This is paid by the airline and will be included in the price of your ticket. It is not an extra charge. The amount varies according to the distance flown and ticket type. This can sometimes mean that intercontinental flights from the UK are noticeably more expensive than those to the UK or from other countries.

I would exit from the airport of whichever city you are staying in last, Amsterdam or Edinburgh. Both are easy to get to from the city. Amsterdam Schiphol has a rail line from the city, Edinburgh airport has a tram line.

You should search for multi-city fares since you are arriving at one place and leaving from a different city. Not sure you’ll find nonstops from Edinburgh to Baltimore; Amsterdam-BWI may be more likely.

The budget airlines like WOW sell reasonably priced one-way tickets, but for many other airlines the one-way fares are through the roof!

You do not need to be concerned about additional fees if you book through an airline or a site that includes all fees. Other than someplace like Turkey that makes you buy a Visa on entry, fees are included in the ticket price, so if the ticket is the right price, then do not worry about it, go with it.

Smaller airports may be easier to use (there are arguments both ways; the staffing may be smaller too.) The big places like Heathrow serve more airlines, especially long-distance routes, giving the traveller more choice both in flights and in transport to the airport. Depending on where you want to go in the United States, you may find that the route from Edinburgh requires changing planes in London anyhow. Amsterdam is an international gateway like Heathrow with easy public access. I suggest shopping with an multi-destination search function, and also with an open mind to find the easiest itinerary at a price you can accept.

PS: www.skyscanner.com will show you no-frills one-way flights from Edinburgh to Amsterdam. Some of these airlines do not show up on airline sites oriented to the United States.