The start up business would be a small fitness studio with personal training. what equipment would be best to start with?

This depends on the type of training you will be offering.
What are the needs of your clientele?
What is your area of expertise?
Who is your target market?

I have seen personal training studios jammed with machines and others with a TRX, free weights and a Bosu

Writing up a business plan and outlining your services is advisable.