My wife and I are members of the Y. She uses a trainer, the machines and pool. I tend to use the machines and some free weights...and usually push my limits at least one session a week (to the chagrin of many of the other retirees). We go to the Y despite having a fairly complete home gym...it seems to motivate us more.
After doing this for >30 years, I know to back off when my joints report back the next day. I do have a daily base set of things I like to do, but mix it up with other machines/lifts because I can or because the joints say so. Seems to work. I do not see a correlation to improved biking ability though...may need to increase leg days.