There are primarily just a few reasons for blade wander:
1. Blade isn’t sharp! Get yourself a high quality blade, just buy from Tuffsaws.
If the blade is blunt it will wander, it’s one of the primary indicators your blade is ready for a change. If it’s a new bandsaw, ditch the blade it came with; it will be rubbish.
2. A duff, but sharp blade. If the set, (bend of the teeth away from the centre line) isn’t consistent and even on either side it will wander. Again buying a blade from Tuffsaws usually eliminates this concern.
3. Blade tension, this is a big issue. Not enough tension and the blade will wander. Most bandsaws are incapable of tensioning up the width of blade the marketing idiots have stated. Typically they can actually tension a HSS blade that 3/4 the width the spec says and about 1/2 the spec for say a M42 blade.
@Sideways and I wrote a thread about refinishing a SCM S45 where we detail the technicality of just about every aspect of a bandsaw. I’d recommend a read.
4. Forget all the marketing rubbish about blade guides. They have ABSOLUTELY no effect on cutting straight. I wrote a thread on bandsaw blade guide theory, again worth a read.
If the blade is too fine, ie teeth count too high the gullets of the teeth can’t accommodate the saw dust if you cut too thick stock. When the gullets become full the blade stops cutting effectively and the blade wanders and blunts.
5. Lastly, assuming tracking is correct, the last issue is forcing the stock through the blade. Again this doesn’t allow the teeth to cut properly and the blade wanders and dulls. Another good sign the blade is dull.