As William notes your market is key.
A "high-end pro" is an ambiguous term but it seems you are implying a wedding or portrait business.
If so, the portrait business yields high per-session sales by being a very personal and hands on business. The business is less about the photography than the sales effort.
That said the entire marketing effort is one that is informed by the brand you establish. Form your premises to your products to your website and your process for meeting and booking clients and of course the quality of your work. Post session follow up is also key to create that relationship that yields large sales.
All this also applies to the wedding field.
Your website is but a part of that.
I would also note that online sales portals are the province of businesses that rely on volume.
A studio that needs high per unit sales will die a swift death relying on online orders. This is because portraiture is an emotional event. Time erodes the emotion that moved the client to book and thus results in low sales.
Sports and events are not high end. They are volume markets.
Fashion and editorial are closer to high end but one markets to them via range of efforts including but not limited to: Instagram, promotional mailers, cold calls, networking and your website. Note I say closer because a vast amount of work produced in this area is unpaid but can be very decently paid.
Advertising, Architectural, product and other forms of commercial photography are where good money can be made. However these clients rarely if ever order online.
I do deliver digital files to clients but only after they have selected images and paid. I use Dropbox but have increasingly used ShootProof. Shootproof can be configured to allow clients to order images or prints. Of course then that means you need to upload fully retouched images to the gallery.
I use Tave for studio management and it has online portals for contracts and booking in addition to scheduling, invoicing and general financial functions.