I would like offer my experience with the most important saw in my shop.
Next to my lathe and bench grinder the band saw is the tool I use the most. My experience is that wood is everywhere for the asking. Neighbors are happy for you to take wood from downed trees off their hands. This can vary from large limbs to major trunks.
With a chain saw, also an important saw, I cut the fresh wood to lengths. Then I use my bandsaw to rip the pieces in half through the center growth ring. With the band saw I can cut a circle which will fit on the bed of my lathe. I find my 14 inch Delta is good for smaller projects but I rely heavily on a 21 inch Grizzly band saw which will cut bowl blanks 14 inches thick. My advice is to get the largest band saw you can afford. With the two saws I find I don’t have to waste so much time changing blades. I use a 1/2 inch blade on the large band saw and a 1/4 inch blade of the smaller saw. The thinner the blade the tighter radius it will cut.
As most experienced turners know, there are many non-commercial wood species which possess beautiful grain patterns and colors. With a band saw you can experiment with these different woods and may find many treasures lurking in wood that has been rejected by commercial loggers. Further, wood with wild grain patterns tend to be rejected by loggers and these may be of the greatest interest to turners. With a band saw you can rip a crotch piece of wood to discover what is inside.
As I don’t limit my woodworking just to bowls, I find the band saw invaluable for ripping out small planks for making spoons and other treen ware. In addition you can rip out turning squares of various dimensions for turning rolling pins, boxes and cups. What may start out as a candidate for a bowl blank could have a defect
but the same piece may be suitable for the non-defective part to be ripped into planks and turning squares.
Just a word of caution. The band saw may make re-sawing so easy that you cut more wood than you have room to store and dry that which is not turned green. Treen ware is not critical due to the small size of the spoon or spatula and it tends to dry without difficulty though I prefer to shape it when dry. However, when you turn lidded boxes out of wood it must be absolutely dry. If not, you may find that a perfect fitting lid just off the lathe will not fit after the parts dry and warp. So if you rip the turning squares you need to have a place for them to dry for a year or two depending on the thickness of the square.
So, get a band saw. If you cannot afford one make friends with someone who does. It is certainly a saw that can be shared. It used to be that lumber yards had a bandsaw where you could get wood re-sawn. I was visiting my son in Ojai, California this February and the local lumber yard did not even own one. I finally was able to track down a local contractor and he was happy to let me re-saw some olive wood for the price of a new bandsaw blade.