Personally, I use wire cutters to free my minis from the sprue, and then a knife to clean them up.
My suggested first purchases:
Primer. Brush on is fine until you decide you want to paint a horde. Most people prefer working from black.
A decent paintbrush. GW makes nice enough paintbrushes. If you look after them, they will last you quite a while. When they no longer hold a point, they can be used for glue and drybrushing. I use a basecoating brush for just about everything. To pick your brush, you want one that has a nice point and no stray hairs. Art stores have a water pad you can use to test the point on your brush.
A hobby knife, med or light duty. These are the ones with the metal handle you carefully insert triangle blades into. You're not doing tank surgery, so a light duty knife will work fine. You can use this to scrape mould lines from your plastic models.
Paint. You can use dollar store paint, just don't expect to win any awards with it. Dollar store paint does make great scenery paint, though! You will need to thin it, and this is why experienced painters prefer expensive paints. Dollar store paint doesn't thin neatly with water, it gets really thin and leaves chunks of paint. This is especially true with metallics. I used dollar store paints on my first minis. Not amazing results, but I was happy. I still use them to paint bases on my minis. Reapermini.com has nice thinning instructions.
Super glue/plastic cement: Plastic cement creates a chemical reaction that melts the parts together. It is a tough bond, but it is permanent! Be sure to test fit! Super glue works for metal and plastic models. You may want to purchase an excellerator, which is a spray that chemically hardens the bond. I buy dollar store super glue, but it dries white, so I am careful where I apply it, or I glue then paint.
A lamp: Personal preference here, but even a desk lamp will work. I find there is just never enough light where I paint. If you use a daylight bulb, your colours will be more natural. I find they look brighter under a regular lamp, then am disappointed with how dark they are when I shut off the light.
You can buy the "Painting citadel minis" book if you like. I use it, but it refers to GW paints. A lot of the material can also be found on youtube for free.
Things not to buy:
A water pot. Use an old cup or a disposable one.
A fancy paint palette. Use a ceramic tile, old CD (yes!) or even a plastic plate.
Modelling sand. Just go down the back alley and sift some gravel, or find a sandbox or go to the beach.
ps: riders just sit on their mounts. You can glue them on, or just let them sit loosely. GW plastics like warg riders and rohan riders have a plastic bit that inserts into a hole in the mount's back.
Have fun! Remember there's always room to grow with your skills and don't be too hard on yourself!
