Advice really depends on the drain material, design, and what's blocking it. Drain cleaners have their place but don't always work. On older drains it can damage them.
Likewise snakes/augers don't always work either for many reasons. Bad angles, "self healing" clogs (the snake cuts a small hole through the clog, but it collapses as the auger is pulled out).
If you already have a high pressure cleaner, a hydrojetting attachment is cheaper than an auger and not only works more often, they completely unclog the drain. If you don't, well sorry, good high pressure cleaners aren't cheap.
Unfortunately, you may have to try a few things to find out what works for you. I'd start by testing how much water goes down to see how far the clog is. If it's not far, you might be abe to dismantle the pipe and clean it by hand. Next I'd try the bicarb and vinegar trick. If I was sure I had a modern pvc drain, I'd give drain cleaner a go. If none of that works, auger or hydrojet, then finally, a professional.