Bike suggestions for bikejoring

Hi there, I hope this is the right forum to post in! I know very little about bikes and am looking to get into bikejoring casually, which is essentially sled-dogging but with a bike instead!

I'm finding very little practical information online about what bike would work best. I would mostly be riding on bikepaths and trails, and wouldn't be doing anything extreme. I'm short (5'4) but not at my best weight at the moment so I'm not sure what bike would work best. Because I'm only planning to ride casually and every weekend or second, I'm really hoping not to spend more than $500. I'd also love some suggestions of bikes I could get secondhand!

Thank you so much :)