If you go to Tacoma, I suggest going with a minimum of equipment. There are some pretty rough neighborhoods on the distant hills that overlook the BNSF yard, but if you don't give the impression of being an easy mark, I think you'll be just fine. The area around Freighthouse Square has always felt safe to me (during the day) and there are some overpasses of the rail tracks that are good for photographers.
The Amtrak Station is about 3 blocks from the Sounder Station at Freighthouse Square. If you arrive on Amtrak from Seattle, go through the station and walk towards downtown on Puyalllup Ave. When you see the small transit center/Greyhound Station, climb the stairs and walk through the parking garage and you will see Freighthouse Square and the ROW for the Tacoma Streetcar to downtown. The Streetcar is free and runs every 10 minutes, so it's not a waste of time or money--except that there's nothing of interest in downtown Tacoma other than the old Union Station (now a federal courthouse).
From the Freighthouse Square/Tacoma Dome station you can take ST 574 to the Airport Link Station and ride Link to downtown Seattle.
One other note: it sounds like you will want to purchase an ORCA card when you get to Seattle. They cost $5 and you pre-load them with money to pay for transit fares. The advantage of having an ORCA card is that one fare is transferable from one agency's system to another's. If you pay cash, you can't transfer from Pierce Transit to Sound Transit to Metro Transit with one fare payment, you will have to pay 3 times. But with the ORCA card, the fare paid on PT is transferable for a ride on ST and then again on MT. Any additional fare required is automatically deducted from the balance on the ORCA card. Get an ORCA from the Sound Transit TVMs.