Both ideas will work just fine. The beater will probably be capable of carrying more via a rack if that matters to you down the road, and also will likely give you the ability to run wider tires. The sweet spot for tires in terms of commuting and utility riding tends to range from 28-35mm wide. From that general range you can choose what's ideal for your needs based on your weight and the road conditions you intend to ride in. Schwalbe Marathons (there are various flavors), Specialized Armadillos, Continental Gatorskins, Pasela Panaracer Tourguards and similar tires are recommended for their puncture protection. Going tubeless will work, but it's not something that is generally seen as essential.

If you go with a 2nd wheelset, the 'Vuelta' brand from Nashbar is often recommended. There are various flavors available depending on your needs, from more heavy duty wheels with high spoke counts, to lighter and 'racier' models.

My opinion would be that going with a (mechanically sound) beater would give you a bit more options. For instance, you would have a second bike that you can rely on should the 'mainstay' be in the shop or otherwise unavailable due to an untimely mechanical issue. Having said that, being retired you are presumably not tied to any strict schedule, and therefore the 2nd wheelset option is also quite viable.