There are two different blue lid buckets of compound commonly found on the shelf/pallet at your local home center: light blue and dark blue, which represent Topping Joint Compound and AP Joint Compound.
Pay attention to the name of the product. The light blue lids are on the buckets of Topping. You don't tape with the light blue lids. It says so right on the bucket. It is for finish coats only, and sands nicely.
You tape with the green lid, also known as all-purpose or "AP", or the darker blue lids, which signify Joint Compound. If you get confused, read the back of the bucket.
As for the mesh tape, it is self-adhesive. There is nothing wrong with using it for the flats, but you'll want to use paper for the corners (including the wall-ceiling joint). With *paper* tape, you lay a bed coat of mud first. Stick the *mesh* tape directly to the drywall - there is no bed coat application until *after* the mesh tape is stuck to the wall.
There are red lids on some ceiling texture and plaster products as well.
There is a big difference between the ready-mixed compounds and the setting-type compounds. The latter dries mostly as a matter of a chemical reaction, while the former dries mostly as a matter of evaporation, and is referred to as "drying-type". The setting-type compounds are stronger, and are used by many for the bed coat. They do dry faster. They come in powder form, but be aware, there is also a drying-type compound that comes in powder form, though I've yet to see it on the shelf.