You can learn a lot with just a snare drum.
The absolute bare minimum to learn the basics of modern rock/pop/funk/etc. kit drumming is snare, hi-hat, and kick drum.
The most popular starting setup for someone learning to play a drum kit is a student level five-piece set that includes snare, kick, and three toms, plus a cymbal set that includes hi-hat, crash, ride, and sometimes an additional cymbal like a splash or china. Many times not all of the necessary hardware (e.g., cymbal stands) is included, so that is an extra expense. Thrones, sticks, extra heads, etc. are rarely included. You might get a free cymbal bag with the purchase of a cymbal set. In the USA, the new (i.e., not used) price for a five-piece kit plus a hat, crash, and ride cymbal pack and necessary hardware will likely end up between 600 and 1000 USD, more often on the higher end of that range for decent equipment.
One thing I would avoid in terms of cymbal packs are packs that include a "crash-ride" cymbal instead of a ride cymbal. Personally, if I were going to invest money in a cymbal to use as a ride cymbal, I want it to be an actual dedicated ride cymbal. The ride is arguably the cymbal with the most articulation options, so compromising it with a "crash-ride" design would be a detriment to learing the nuances of playing the ride. Plus, eventually one would want a real ride and a second dedicated crash, and at that point a "crash-ride" is most likely useless.
The minimum quality would be good enough to not fall over when struck, drums should be tunable and actually sound different when struck dead center versus at the edges, and cymbals should sound different when struck with the tip versus the shank of the stick. Any quality above that would be unlikely to be appreciated by an absolute beginner, but may serve as further inspiration and enjoyment of playing.