Swiss Travel Pass

That is correct, I would not bother with seat reservations, Swiss trains run so frequently that there are almost always open seats, and other people don't buy them for that reason. Exception might be a holiday weekend, big city commute times. Also 1st class just gives a bit more room, which is already plentiful in 2nd class. The pass also includes urban transport in most Swiss cities, and free admission to many museums.

But if you are looking to save money, it is often not the most effective solution. The Half Fare Card for 120 CHF for a month will often give more savings. You still have to buy a ticket for each journey, but it is always 50% off, even for city transport. Some places it is even better than a Travel Pass. The journey to the Jungfraujoch above Wengen is only a 25% discount with the Travel Pass, but with the HFC it is 50%. The Travel Pass does cover, at least for this year, the Schilthornbahn all the way to the top above Muerren.

I understand the Swiss Rail Pass covers most of the rail lines

All of the rail lines, except some mountain railways. See the official map (you will get a copy of this with your pass): https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-sts-pass-gueltigkeit.pdf

and you pay extra for a reserved seat or upgrade on class.

You don't need to (and usually can't) reserve sets on Swiss trains. If you want 1st class (which I think is unnecessary), get a 1st class pass.
If you have a pass, you just get on a train (or bus or boat), and show your pass when the ticket inspector comes around.

Will this pass also cover transportation to & from Old Town Zurich to Zurich airport?

Yes, all urban transport in all Swiss cities. Zürich airport has its own station (called "Zürich Flughafen"). You catch a train direct from the airport to anywhere in Switzerland.

We are planning to purchase the Swiss Pass since it covers most of the train travel and some additional lifts & boats. Any comments will be appreciated.

Yes, as Sam says, a Half Price Card (plus buying half price tickets) may be cheaper. You have to do the arithmetic yourself.

Swiss Travel Pass covers you 100% from Lauterbrunnen to Wengen and also from Lauterbrunnen to Murren on the other side of the valley. It also covers you 100% from Murren onwards to the Schilthorn at 100% in 2018.