Woodcarving is pretty simple when it comes to tools and equipment compared to it's big brother woodworking. You can get a lot done with very little - for example some purists carvers only use one knife and wood that they find fallen in the forest. I've put together 5 things that I consider the bare essentials for carving, with a focus on figure carving or carving-in-the-round.
I recommend Basswood as the best wood for beginner woodcarvers. You should look to source your wood from local hardwood suppliers/sawmills as you can pick out your wood in person. Online options are available on Amazon in precut blanks of various sizes, here and here. Some other woods I like using are Walnut, Cherry, Butternut and Maple.
I use two Japanese pull saws (a Ryoba and a Dozuki) and a coping saw in my apartment workshop, but if money and space were no object I would be using a bandsaw, which is by far the most efficient way to cut out your carving blanks from raw wood. Other options are tenon saws and scroll saws, basically anything that will cut out your basic rough shapes.
My recommendation for a beginner is to get one good knife that will perform well in all areas of the carving, and a good example of that is the Flexcut detail knife. I like a 1.5 inch blade on my knives, and a nice fine tip. I currently use a Ben Orford handmade Big Pick Knife, (which is pricier). Other cheaper options are exacto/scalpel type blades or interchangeable blades.
Other links for knives that I'd recommend:
Mora 120: https://amzn.to/32MSyNx
Interchangeable Blades: https://amzn.to/31zATsr
Whittlers Kit: https://amzn.to/2O7YpZN
A chisel is key to getting good smooth forms and easy roughouts, especailly in harder woods. I think it is important to have both a chisel and a knife, and learn how to use both as the cutting action with each tool is very different and will improve your carvings. I got a lot of my favourite plain chisels at second hand markets and sharpened them up myself, so don't be afraid to shop around, as a chisel is a simple tool.
My favourite: http://bit.ly/2kFryiM
Pfeil #3 gouge (I like a 25mm): http://bit.ly/2kSgWwX
Pfeil Chisel: http://bit.ly/2kGyJHt
5. Finger Protection
Chisels and knives are very sharp objects, and when starting out finger protection helps not only for safety but also for confidence. My preferred method of finger protection is friction guard tape on my left hand index and middle fingers and thumb. Other options are a full carving glove often made with stainless steel weave, or individual finger guards, however I feel this hinder my dexterity and are detrimental to my carving.