I haven't been to Fürgangen-Bellwald myself (yet!), but the following thoughts come to mind:
- Brig has much better transport connections if you intend to travel around a bit
- Brig has better options when the weather is unpleasant
I wasn't sure whether you meant you were thinking of staying near the Fürgangen-Bellwald railway station/cable-car station in the valley, or in Bellwald up on the mountain.
If Bellwald on the mountain, it seems you will need to travel up and down by cable car each time you want to go somewhere else (6 minute trip). Return fare for adults is CHF 13,60; for children aged 6-16 CHF 6,80. If you have a Swiss Travel Pass or Half-fare Card, you get a 50% discount, and it seems you can also get multi-trip tickets at a small discount.
I got this information from the website below, but it is only in German:
The "Preise" tab has prices
There is also a timetable on that site ("Fahrplan")
The "Revision" tab has details of service interruptions to the cable car service due to maintenance. That includes the first Tuesday of each month, as well as the half-yearly maintenance period 21 October to 5 November 2016 (except for 30-31 October and 1 November). A bus replacement (12 seats or so) will be in place for the October-November maintenance period.
There's a panorama map here, that gives you a good idea of the lie of the land if you haven't seen it already:
Bellwald apparently is designated as a family-friendly resort, but it's not clear what would actually be on offer in October, which would be between seasons.
Hope you find this helpful.