Help selecting between wire/folding tires I’m hoping someone can help me decide whether to go with the wire bead type or foldable Kevlar. 

What are the advantages/disadvantages of each? 

The bike is an old Fuji that originally came with 700x19c tires. 

I’m not an avid biker just riding around on bike paths mostly on weekends. Maybe ride about 20 miles a weekend, but since I’m in the market for new tires I’m looking to purchase wisely. Thanks
For most of us it makes little difference.

Kevlar beads are supposed to be harder to fit but the hardest job I've had fitting tyres has been with wire. Some tyres are available in both (there's normally a little difference in the compound as well). The kevlar version is nominally more expensive, but can be cheaper if it's stocked in more competitive places. I found this with my winter tyres. As the kevlar version folds it can be cheaper to ship as well.

The weight saving of kevlar is real but small enough that you're not going to notice unless you're racing at a high level.