If the gym is small, you'll find they’ll go for a small selection of machines to cover most of the muscle groups and then a maybe a dumbbell rack. They'll see this as having everything covered.

Big gyms, on the other hand, are likely to have free weights area which will include both dumbbells and barbells.

Gym chains generally put machines first these days as new gym goers don't need much instruction to get the most out of them. Plus it's far easier to see quick results and less hassle for the instructors.

Unless you specifically want a gym that is free weight oriented, I advise you to sign up with a chain as they have the money to stock up on enough of the right equipment.

There should also be plenty of instructors around so time issues shouldn't be a problem.