I couldn't advise the best set for a beginner. I train at home now but it took me a number of years to find a direction that made this level of outlay worthwhile. If I had known in advance I could have saved a fortune in gym fees, but I would have likely bought things far too light duty seeing my current strength as something impossible so not worth spending the money anticipating.
Goldie will hate me for this, he loves his perfect olympic size discs but I don't see any specific value to these unless you want to compete. My heaviest discs are 25kg and smaller than olympic standard. My deadlift starts with the bar closer to the ground which is harder, I like this, because I am weird.
If going for free weights get a safety rack that will withstand at least 6 times what you anticipate your maximum ever lift to be. This way if you drop the weight the rack will catch it, and you will drop to the floor safely embarrassed but alive. You may never need this level of safety but better to have it and not need it than need it and not have it.
Free weights are better in virtually every way, the one exception is minimising risk and if training alone at home this has to be considered. Ironically however it is a cable clip that last damaged me in the gym, but that was a cut thumb, not crushed chest.
Training on machines is more limited and isolated to individual muscle groups, because it is more stable and controlled by the mechanisms. With free weights you provide the stability and control which engages more muscle groups giving a more balanced workout. You are also able to do more exercises with less kit.
Brand wise, totally opinion based. I went for such a simple set up that brands made little difference, an iron disc is an iron disc, as long as it's the right weight I don't care. The rack I was fussy about, kettles had to feel right in my hand etc. but that was totally personal.
If going for machines, especially multi-gyms check every movement and how appropriate the weight stack and intervals are before buying. I have seen people buy something where the stack was enough for bench and pathetic for squats, and the intervals on the low weights was too large for the isolation movements. Think about what you want or could want very carefully.
Consider space available. Free weights are deceptively space hungry especially when adding bench, rack and allowing for loading space. Look at cardio gear and if it folds find out how it feels when unfolded.
Think forward.
If you will only ever be light duty and just want to do some basic stuff go light duty and save some money, but make sure it's comfortable.
If you are a light duty trainer but want to get reasonably into it, go medium duty, light will fail you after a while or just feel horrible.
If you are the sort of person who will not quit until you are practically dying get heavy duty gear. It is expensive, but the alternative is buying and breaking light duty then spending out again.
With new year resolution season just finished you will be able to pick up bargains second hand or new as people sell the expensive clothes hangers and fitness shops see their seasonal glut come to an end. I am not a nice person when buying large items and negotiated prices and upgrades of kit making a finished result of about 60-70% of shop prices, which were already 'reduced' compared to rrp. No-one in their right minds pays rrp.
