I am using a near 40 year old cast iron bandsaw I bought off craiglist in my own garage shop. When I got it it was nearly ready for the scrapheap (in appearance) and It had similar cutting issues - actually much much worse. After rewiring, cleaning off some rust and using youtube to guide me on setup/alignment. It now cuts like a dream.
Short of it is: bandsaws can be finicky. Rarely do any of them perform to their potential out of the box (short of maybe some of the big budget behemoths)...but they're also pretty simple and very durable. There are a ton of DIY tweaks people do to "tune" them/ In your case, the ridges you mentioned could be from the vibrations or blade, but more than likely they are result of either alignment of the wheels or the guide blocks. both can cause some tracking issues and cause a blade to wander. You can test a lot of these setup issues with a level and a square -- and a little bit of youtube browsing. There's tons of good info.
One tweak I'd recommend regardless - You can replace the stock guideblocks with some of the aftermarket ones (Cool Blocks is the brand I know). These are inexpensive and generally help you get a smoother, cleaner cut by reducing friction.
As Dream Burls mentioned, there is also a lot of science to blades. Here, the blade probably isn't your issue - but which ones you choose will matter for accuracy, durability...and for any curves you cut..so it may be worth looking into. The blade science stuff focuses on what material you are cutting (hardwood, softwood etc), type of cut your are making (resaw, ripping, curves/scrolling) and durability of the blade. You'll see references to different teeth per inch, blade width, tooth pattern , cut finish (rough/smooth) etc