Is it possible to do weight training at home that is comparable to a gym?

At my apartment complex, I have access to many cardio machines (treadmills, ellipticals, & stationary bikes). However, they do not have anything for weight training. I know how important it is to combine cardio and weight training so I joined a gym. I currently belong to LA fitness, and I absolutely hate it. As a college student, it is the only gym in my price range, but I am really unhappy with the place. The lines for the equipment are ridiculous. It can take up to 20 minutes to find a parking spot. Also, I feel really uncomfortable in the weight training section because it is mostly men. Not to mention, many people at the gym have no clue what they are doing and will spend 40 minutes doing squats or hours on one bench. Because of this, I am not able to use machines, weights, and benches I want to use.

Is it possible to do weight training at home that is comparable to weight training at a gym? I do have a strong knowledge about proper weight training. I own adjustable dumbbells at home that go up to 25 pounds and a jump rope. The gym at my apartment complex also has an adjustable bench. Will I be missing out on a lot of exercises by not having access to some of the machines? I have a petite frame and my goal is to become more toned and strong. Living in an apartment I do not have the space for large equipment, and I also can not afford it. However, I would be willing to spend money on other types equipment (such as a medicine ball) that could further help my fitness goals. I am worried that if I cancel my gym membership and weight train at home I will not be able to see the results I want to see.

Thanks for all of your advice - I really appreciate it!

I guess a major concern of mine is that I don't have all the equipment, a ton of different weights, or barbells. Can I make-do with the little equipment I have now, or do I need to make other purchases?

yes.
i live in an apartment and have a barbell,dumbells,and over 300lbs of weights in my bedroom. nothing has help me more than training books that detail every aspect of successful weight training from how to eat to how to train correctly. i don't have to know anything other than how to find the experts who already know what to do.
i hate gyms for mainly two reasons. i have seldom been when someone doesn't hog a machine or act like a jerk and people sweat all over the equipment
big plus of home workout. i can usually do a workout in the time it takes to drive to and from the gym.
i have found that cardio isn't necessary for fat loss if there is very little break between sets which keeps my heart rate constantly high.
//25lb dumbbells are heavy enough ,especially if you do slow repetitions where you don't use any momentum and make smooth transitions up and down. i have the amount of weights i have because i use to do deadlifts and kept purchasing plates the stronger i got.
other than deadlifts i seldom lift more than a 100lbs. since i lift the weights slow for usually 8 to 12reps.

Yes, if you know what you need and how to use it and have the space go for it.
Your results are dependant on you doing the exercizes correctly not which machine you use. Many times there are weight training movements that give the same benefit of a machine.