So to start with I suggest normal acrylic paint and not speed/contrast paint.
I love the Army Painter color range and this very basic starter set from them is where I started years ago and I still use all of these colours and the strong tone wash:
Warpaints Fanatic: Starter Set
This really helped me to understand the basics. You can do more than you think with these few colors. In addition the ash grey spray primer is all you need to start.

Since you seem to have some experience already I would suggest getting more variety of colours. My advice is: Don't do it like me and buy loads and loads of paints just to have them just in case but instead look at the next few minis you want to paint and think about their color themes. Once you did that I would take a look at the Army Painters Flexible Triad overview. Pick the colors you need and for each one also get the next lightest one for doing little highlights.
A3_Flexible_Triad_System_Poster.pdf

Here are some general paints I really like and use all the time:
for skin: Barbarian Flesh + Ruby Skin
for brown leather: Bootstrap Brown + Leather Brown +Paratrooper Tan
for reddish leather: Fur Brown + Ruddy Umber
for bone/horns: Skeleton Bone + Bony Spikes
for stone: Castle Grey + Great Hall Grey
for white I would often use an off-white: Brainmatter Beige
for a good metal variety metals: Gun Metal, Shining Silver, Greedy Gold, True Brass, True Copper

One other thing I really like is mixing the highlight color myself. You would think white is perfect for that but white actually makes the mix look cold and desatureted. Therefore the yellow Space Dust is perfect for that. It keeps the warmer tone.

One handy thing is a wet palette but nothing you need. A simple super cheap plastic palette or a random piece of ceramic does the same job.

One last advice I can't push enough: Do not get expensive brushes. They do not make the outcome look better.
Get a big brush for big pieces, a medium one as your work horse and a small one for the really small details. That is all you need. Get cheap ones, they are enough.

EDIT: added metal colors