Well if you have a good space for the gym I would recommend in this order
olympic barbell + plates. get a seven foot bar to use in the power rack.
power rack - this is the best item. the safety bars will help save you especially if training alone.
a bench. get one that is easy to adjust. it does not need anything fancy on it but should be strong.
adjustable dumbells - olympic size so you can use the same plates as the others.
a storage rack for the plates - best thing I ever got. but some racks have this built in.
I am all for the home gym. commercial gyms can have many problems, you add the time to commute there, you have to re-rack weights and wipe things down etc.. what a waste of time, and most have stupid policies and rubbish gear - so then you have to find a good one.
At home you have total control of what you do, when, music, etc.. it is much better.
The biggest problem is if you buy all the stuff and then decide you don't want to do it, but you can usually sell it again if needed, especially quality stuff.
I recommend this book
For anyone starting out to read and also Starting Strength for technique in the important lifts.
T-Nation is also an overwhelming wealth of resources.