I like having a brush for foundation/tinted moisturiser - I like the Real Techniques Expert Face Brush or the Buffing Brush. They are quite similar IMO. I like using a brush as I think it looks better and if I add too much blusher later, I can go back with the foundation brush to sheer the blusher out.
For eyeshadows, I like the Mac 217 brushes as well as a brush for eyeliner.
I think it's very individual what works with liner - I have always been recommended an angled brush, but I just cannot get liner to look like with that brush. Instead I use a Mac 210.
If you would rather not do cat eyeliner/flicks, then a push liner such as a Mac 212 works well - I use this a lot for everyday makeup.
A powder brush for powder is nice as powder puffs can apply too much to the face and make it look too powdery. I just like a big fluffy one - I have a Mac 150 which has a great size and shape, but it sheds a lot which isn't such a flattering look.
A blusher brush is also nice to have - I like the Real Techniques one. Mac 167 is also quite nice, and smaller ones such as Mac 168 or Laura Mercier Cheek Colour brush are also nice.
For eyebrows, I like an angled brush and a spoolie (a classic mascara wand).
There are many cheaper alternatives available :)
Personally, I really like cream eyeshadows (Laura Mercier Caviar Sticks, Mac Paint Pots, Chanel Illusion d'Ombre, Rimmel Scandaleyes - many other companies make them too).
They are easy to apply, come in loads of colours, can be sheered out for a day look or built up for a more glamourous look and last really well.
I apply the stick/pencil type by drawing on the lid (not too much - can always add more if needed), then sheering out with a brush. The ones in pots I apply with a brush, a little at a time.
I think powder blushers are easier to work with than creams/gels/liquids, but it might be a matter of habit. The Chanel cream blushers do seem very nice though.
If you're looking to buy a new foundation, then ask for samples before buying as they can be expensive and if they aren't right for you, it's just a waste of money.
If you want ideas for products or certain colours, then it might be worth describing your skintone, eye colour, hair colour and what kind of makeup you'd like.