Where/How should I fuse this transformer?
Your transformer has 0.35A rating for its secondaries (each). You can fuse those with a [say] 0.3A fuse each. (The center tap doesn't nee a fuse.) The fuse in the primary [if you want it] needs to be much smaller. For 115V primary, you have a turns ratio of about 3.20 (to both secondaries in series), so the max current in the primary is about 0.11A. A 100mA fuse should work there.

Beware that if put the secondary side fuses after the rectifier they need to be DC fuses. AC and DC fuses are not the same because the latter need to cut the arc while in the former it gets cut by the AC sinewave itself.