re: Workout routine recommendations for a 55 year old

Start lifting weights 3 days per weak progressively, with a barbell or dumbbells or even if you wanted use gymnastic rings

Walk for a hour 3 other days

Eat in a caloric deficit
Eat your bodyweight in grams of protein, literally

For a plan, an linear progression program will work for barbell. I always suggest 531 beginner prep school for older guys. You can google to find spreadsheet.

For dumbbell, I like ppsa db strength. 1st month start with just first two super sets, then add the third the next, then the 4th then the cardio section.

For bodyweight, I suggest gymnastics rings and following body by rings. Then do lunges, reverse lunges, rear foot elevated split squats and body weight squats for lower body.

And walk a lot. Try and get 10-12k steps every day