How to take either of the two options for making the journey from Basel to Bellinzona (fast or scenic)

Final Destination: Locarno

These trains also call at: Goschenen (connect for the MGB trains to Andermatt and beyond);
Airolo; Faido and Biasca

Book early and save: Yes

These trains are operated by SOB and tickets can be booked on its website.

Tickets are also sold on the SBB, Swiss National Railways, website and on its website, journey times, departure times and prices, can be compared with the alternative, faster trains operated by SBB.

When booking on the SBB website there are two things that are worth looking out for:
(1) If you want to to specifically travel by these trains on the more scenic route, look for IR in the ‘travel with’ column and the red % button in the 'Fare' column.
(2) Cheaper ‘Supersaver’ tickets (those with a % symbol on a red button) are available on these IR trains between Basel and Bellinzona.
You’re most likely to find these Supersaver tickets if you book around 4 - 8 weeks ahead.
You may need to search through the departures to find these 'Supersaver' tickets using the ‘earlier’ and ‘later’ buttons, so try and be flexible with your departure and arrival times.

Using Eurail or InterRail Passes

These trains connect in Cadenazzo into 'Ticino' regional trains on to Milano via Como.

If you have a Eurail or InterRail pass, taking these trains and making the connection will be a much more scenic option than taking the direct EC trains between Basel and Milano AND you can also avoid the rail pass reservation fees charged on the EC trains.

Final Destination: Lugano or Chiasso - the IC trains; Milano or Genova or Bologna or Venezia - the EC trains

All trains also call at: Arth-Goldau

The train service between Basel and Bellinzona is split between:
1: IC trains - that are slightly slower, but also generally cheaper than
2: the EC trains that call at Bellinzona on route to Italy
3: The slower IR train services.

Note that a mix of trains is used for these express services, most common are the new Giruno trains, which on this route are used on many departures which don't cross the border to Italy.
Though on this route, the Astoro trains are typically used on the trains which head on to Milano.

The timetable is is arranged so that in the odd hours these express trains depart Basel for Bellinzona, but in even hours the alternative IR trains provide the direct service.

But if want to be in Bellinzona more than 44 mins before those IR trains will be due to arrive there, you can take those IR trains and make a simple connection into an IC or EC train at Arth-Goldau station.
When looking up this journey, those options with a connection can be cheaper; because the cheapest Supersaver tickets can be available for longer, they sell out faster on the direct trains.

Book early and save: Yes - If you book Supersaver tickets (more info is available on the SBB ticket guide below)

You may need to search through the departures to find them using the ‘earlier’ and ‘later’ buttons; the Supersaver tickets tend to sell out particularly quickly on this route.

Online bookings open: up to six months ahead of the travel date

Try and be flexible with your departure and arrival times, book as near to 60 days ahead as possible and don't be overly concerned whether you will be taking an IC or EC train.

If you will be making a day trip to Bellinzona from Basel, be open to the possibility that Saver Day Passes are likely to be a cheaper option than booking return tickets.

Seat reservations:

Seat reservations are optional on Swiss IC trains and for the journey by EC trains as it's wholly within Switzerland, so seats won't be automatically assigned when booking online.
You can book reservations online, AFTER you have booked a ticket, by using the SBB (Swiss national railways) seat reservation service OR request and pay for a reservation when booking at a station ticket office.

Travelling with a rail pass:

Rail pass users can jump on any train, without having to make reservations, but taking the more scenic route is highly recommended.