Sorry to be a bit blunt in my answer, but the client hired your "e-commerce web agency" to do e-commerce conversion optimization, yet your company doesn't know how to do e-commerce conversion optimization?

Perhaps have a conversation with someone in your company or talk to your manager or the agency principal and encourage them to hire for e-commerce conversion optimization expertise. It's an entire discipline requiring years of experience and track record in driving higher conversions for e-commerce sites (in my opinion).

In lieu of that, how many marketing dollars are going to be spent to drive traffic to the site and who is managing that part? Often new start-ups will spend so much of their dollars BUILDING the site, they don't leave much money to spend on AdWords or other methods to drive traffic to it. The amount of traffic will help determine how many tests to run and how often. Usually we start with two very different landing pages (do you have landing pages?), then fine-tune the split testing down to things like headlines and photos. The checkout pages, especially any pricing pages, are also critical in the testing. Is it a brand new concept or established product/service? If brand new, it will take very well-crafted pages to get visitors to pay money for something (vs. a trial). If established, why is your product best and why should I buy now? You should map out the conversion flows to the confirmation page (success page) and measure the drop-off or conversion rates at each step. Test different elements/pages at each step. Also measure things like average cart size (if more than one product), revenue per transaction and long-term customer value.

Hope that helps. Best wishes to you!