this is still not very specific. I am just making the assumption that it is personal training only with 2 or 3 trainers.
You should have two pieces of cardio equipment. I would go with one treadmill and one elliptical.
For strength, you will need dumbbells and a rack to put them on, 2 sets of 2 up to 15 pounds and 1 set up to …. depends on the clientele. Tubing and bands, ankle weights, balls of different sizes, Bosus and bench(es), mats, a TRX.
As far as larger equipment is concerned, that depends a lot on your budget and clientele. At my studio, I have now a dual axis cable tower, a total gym Power Tower and a Bowflex. If I had to decide again which to get first, I’d go with the total Gym and then the cables. I use the Bowflex the least but when I started, the others were not yet available.
I wish you good luck.