Buying Ferry tickets; boarding the ship; HELP!

You can still do like you did 23 years ago, just bought your ticket at a travel agency a day or two before the ferry trip.

"if I book my tickets on (for example) Blue Star or Seajets websites,
do I get a ticket online upon purchase that I can print? Or is it a QR
Code?"

When you buy your tickets online on the ferry company websites with the webcheckin option you will receive an email with your ticket including a QR code which is scanned when you board.

You can print it if you want a backup, a smartphone breakdown is always by definition unpredictable.

With your ticket in electronic or paper form no other document is necessary

Except for some ferries which do not carry vehicles (the small Seajets catamarans for example) you must place your luggage in the racks on the garage level when you board.

The destinations (names of the islands) are indicated on the racks.

That being said, when there are a lot of passengers there is not enough room in the racks and all the luggage can pile up on the floor. So I adopted two techniques for luggage:

Either I try to be among the first to board and so I can place my luggage in the racks, or I wait until the crowd of passengers have stacked their luggage and I put mine at the end. (otherwise it will be crushed by half a dozen other suitcases stacked on top of mine)

Once the ferry has departed, no passenger has access to the garage level where luggage is stored, but keep your valuables with you.

You can purchase a ferry ticket from any Greek travel agency. Normally we buy our ticket a couple of days prior to the sailing, That way the agent will have full information on strikes and upcoming weather. We have never purchased tickets directly from the ferry company web site.

When you board the ferry you will be on the car deck or main deck. There will be racks with the name of one of the islands on the route that day. You leave your bags on the appropriate rack. Most of the time you just leave your bag on the floor.
When the ferry departs access to that deck is locked.
When the ferry nears its destination the deck is opened up and everyone departing makes a mad rush to find their bags then they go to the exit and wait. It is a good idea to mark you bag with something distinctive, a belt or strap or coloured tape. It can be a bit of a madhouse so spotting you luggage quickly is important.

Being that I will be traveling in August, I fear having a boat be sold out, so I will purchase tickets online months in advance.

As a young adult traveling back in the 1990s, I had no hotel reservations, just went where I felt like, so changing plans last minute was of no consequence. Now with a family of four, the days of "winging it" are in the past.