Is it recommended to find a tour that visits Murano, Burano, etc. or would my wife and I be better off to take a day just going on our own from island-to-island?

I think it would be better to do the islands on your own. I recommend Torcello over Murano and Burano.

I've visited these islands a number of time, always on my own. I see no need for a tour. On your own, be sure to check the vaporetto schedule when you arrive on each island so you can be aware of when the boats will be available for departure so you can time your visit.

I'm with the DIY crowd. if you plan to do the islands, there is a vaporetto service from the fondamente nuove but it is quite pricey to do all three as individual journeys so do get a vaporetto pass at least for that day if for no other.

My favourite between Murano and Burano is burano - the houses are all brightly painted and there are a number of restaurants along the main street where you can sit in the sun and have lunch. then get the little ferry to Torcello to see the ancient Cathedral with its 1000 year old mosaics.

alternatively, go there first and have lunch there - we had a lovely meal at the trattoria Attila - then go back to Burano and Murano on the way back.

as ellenem says, check the ferry schedules as some of them stop at lunch time.

Definitely get a vaparetto pass for as many days as you intend to be traveling around. Half the experience is riding around with the locals, although, in the rush hours, it can feel like a Tokyo subway.

for some reason not often mentioned, we found Lido worth a few hours.
Very different feel than the city......something like a small resort town.

Definitely do it on your own - otherwise you spend a lot of time in a variety of shops that pay the tours to bring the suckers in.

And I agree that Torcello is the most intersting of the islands. This is where the Venetians first went to hide from the barbarians invading Italy in 400 whatever - has an incredible church that is very Byzantine and is much less commercial than the others.