In general, the best place to book Swiss train tickets is the website of the Swiss Railways at https://sbb.ch/en/ or the SBB app. For international journeys, you may find booking portals like thetrainline.com or raileurope.com (or Omio, which you already found) to be more convenient. These sites usually charge a small booking fee in addition to the ticket price.
Some options worth considering besides a regular ticket:
Foreign visitors have access to the Swiss Travel Pass offering, of which the "Flex" version costs CHF 267 for 3 days of unlimited travel within a month. This pass may quickly be worthwhile if you are planning some trips from Zurich. Besides trains, it also includes city transit, most buses, some boats etc. You can buy it from swisstravelpass.com or SBB.
There are supersaver tickets, only valid for a specific connection, at a discount. Rarely available for busy intercity lines unfortunately.
There are also "supersaver day passes" available in limited numbers, you should see them as an alternative option when buying a single ticket from SBB.
Note that the Swiss Railways give no discount for senior citizens (except for some travel passes and promotions not relevant here). Also there is no discount on round trips.
Regardless of the type of ticket you buy, I'd recommend that you make a seat reservation for your journey as Geneva-Zurich is one of the busiest lines in Switzerland. Tickets cannot sell out and you will never be denied boarding, but you may find it hard to find empty seats.