What weights

For my home gym I have a simple set of Olympic weights bought off ebay to keep costs down. I won't pretend that finding a deal was as easy as other might make out as it wasn't.  Olympic weights tend to hold their value and do seem to be in high demand.  

Eventually I managed to get a set for £150 with the following:

2 x 25kg
2 x 20kg
2 x 15kg
2 x 10kg
2 x 5kg
2 x 2.5
2 x 0.5kg

They are rubber coated with tri grip.  Whilst the rubber coating is not essential I would say for a home gym the tri grip is as it allows there to be a number of extra uses for the weights that there usually wouldn't be.  This includes shrugs and farmers walks among others.

I also had a standard silver 7ft barbell as part of the price that it fine for the purpose I need at home.  If you are in to specialised lifting sports, Olympic lifting, cross fit then you may want a more expensive bar that is suited to that sport and has different properties such as more whip or better knurling for grip.

I separately purchased a ez super curl bar new from ebay for £20.  This is for curls, rows other lifter lifts that I will do in my circuit.  This avoids the need for changing weights over on the main bar and lets me move between exercises with more efficiency.  Whilst its not essential as all exercises can be done with the straight bar for the price and minimal space it takes up this is a good add on purchase.

I wouldn't recommender getting anything like a trap bar (the hexagional bars you stand inbetween) or farmers walk/shrug bars at this stage as  they are very specialised and take up loads of room, which in a home gym is at a premium.