I don't think you have the footing or the support to work out in bare feet. I know shoes are expensive but the key is to go to a good, independently owned and run store. We go to a running/sports store where they actually watch you walk down the sidewalk, they look at your old shoes to see how they've worn down, etc. They have a treadmill you can walk on while they watch your feet - they look at your stride, whether you have pronation, and so on. You cannot get this if you go to a sporting goods store in the mall - the sales staff are not experienced. My son and husband are runners, but I am not. The store knows that I am looking for shoes for working out, for walking, for cross training (doing multiple tasks) and that's how they fit me.
I think you need arch support and something to keep you from slipping. It's more than just cushioning. You will get more out of your workout if you If you go to a good store, you'll get the help you need. Tell them you are on a budget - sometimes they will discount things, believe it or not. The shoes will LAST you too. I wouldn't skimp here - I'd buy clothes at the consignment shop and splurge on good shoes. You can wind up with knee and hip problems, back aches, and more.
And toss the old ones - put them in the Goodwill bin somewhere. It may not just be that they are old - they are not properly fitted to you.
If you can't find a store on your own, call the local high school track coach or the head of phys ed, and ask where the kids buy shoes. Our local store gives 10% off to the athletes, and my husband and I got the same discount that our son gets.