Hi waktravel, and welcome to MySwissAlps!
>> July 7, 2017 Arrive Zurich/Lucerne. July 20 depart Zurich for US.
>> Purchase 15 Flex, 1st class
With the amount of travel you are doing, I think a 15-day consecutive Swiss Travel Pass would be be better and cheaper.
How to use your Swiss Travel Pass or Swiss Travel Pass Flex is covered at the links below. You can also download a map showing where your pass is valid under the Where it's valid tab.
As explained in the legend on the maps, red lines are trains, yellow lines are buses, black lines are cable cars, white lines are boats. Solid lines are free, dotted lines are discounted. Discounts are mostly 50%, but only 25% for transport where you see the number "1" inside circle near the dotted line. There are a few grey lines on the maps as well, which indicate transport that is not covered by the pass.
>> reserved single seat
Seat reservations on trains are only mandatory for the Glacier Express, Bernina Express and Gotthard Panorama Express. Reservations are not usual on most other trains, but can be made in some cases where indicated in the timetable.
Information about travelling by train is here:
>> 3rd cl hotels.
You can look for hotels, including budget ones, here:
>> 2 nights Lucerne, Mt. Pilatus
Information about Luzern/Lucerne and Pilatus is here:
>> 1 night Lugano,Gotthard Express, right side of train?
Reservations on the Gotthard Panorama Express are mandatory. I don't think you are able to choose what side of the train your seat is on. There is some useful information here:
>> Bus to Tirano/Bernina Express
Reservations are mandatory on both the Bernina Express bus and Bernina Express train. See this post for tips on transferring between bus and train in Tirano:
On the bus from Lugano to Menaggio, I prefer the views on the right, mainly for travelling along Lake Lugano, the descent into Menaggio, and travelling along Lake Como. I haven't travelled along the sector from the top of Lake Como to Tirano.
Travelling from Tirano to St Moritz, I prefer to sit on the left for the best view of lakes and glaciers, but there are great views on both sides at different times.
There is more information about the Bernina Express here:
>> 1 night St. Moritz
St Moritz Dorf is built on a hill. In choosing a hotel, I recommend you choose one located near a town bus stop, or choose a hotel that offers a shuttle service to the railway station. St Moritz Bad is fairly flat, but you would still want to choose a hotel near a town bus stop for convenience. Buses are low floor.
>> Glacier Express
Reservations are mandatory, and you cannot tell for sure which side of the train your reserved seat will be on. In any case, the train changes direction in Chur. However, with panoramic windows, you get good views regardless of which side you are seated on. Going through the Rhine Gorge, the best views are on the right. Going over the Oberalppass, I like the views on the left best. From Visp to Zermatt, I also prefer the left.
>> 3 nights Zermatt, Matterhorn
Information about Zermatt and the Gornergrat and Klein Matterhorn/Glacier Paradise viewing points for the Matterhorn are here:
>> 3 nights Interlaken, Jungfraujoch.
Travel from Interlaken Ost to Grindelwald or Wengen is free with your Swiss Travel Pass or Swiss Travel Pass Flex. You will need to buy a ticket (25% discount) from either Grindelwald or Wengen (and return to either Grindelwald or Wengen). You can go up one way and down the other, which I would highly recommend, as the scenery is very different.
From Wengen to Kleine Scheidegg, the best views are on the right. From Grindelwald to Kleine Scheidegg the views are great on both sides - the mountains, including the Eiger on the left, valley views on the right.
You can't reserve seats on the Jungfraujoch route between Interlaken and Kleine Scheidegg, but you can reserve a seat from Kleine Scheidegg to the Jungfraujoch and return. In July, a reservation might be a good idea, however I would recommend not buying a ticket or making a reservation until the day before, so you can be sure the weather will be suitable and the views will not be obscured by clouds. Tickets and reservations cannot be exchanged or refunded.
You do not get an allocated reserved seat, but there are separate carriages for those with reservations and those without. Look for the signs at Kleine Scheidegg telling you where to queue and board depending on whether or not you have a reservation.
You can plan your town-to-town trips, as well as mountain trips, with the Swiss Timetable here:
Please feel free to ask further questions after you have read the information I have linked to in this post. Happy planning!