Let's start with the eyes. I find that a cream-to-powder eyeshadow formula tends to have better staying power than regular powder shadows. I don't have particular recommendations for this category, so I invite you to leave yours as comments! I know Revlon also has a line of Colorstay eyeshadows that may be worth a try.
For eyeliners, liquid or gel liners are almost completely budge-proof. I have yet to master the art of liquid liner application, but adore MAC Fluidline ($14.50) and Bobbi Brown Long Wearing Gel Liner ($18). Depending on the kind of brush (and color) you use to apply, you can make the line thick and dramatic, or fine and subtle.
I've heard claims that powder blush stays better than cream, and vice versa, so this is a bit more trial and error (and may have more to do with the texture and oiliness of your skin). But if you really want flushed cheeks that last, your best bet by far is a stain. Benetint($28) by Benefit is amazing. Another good choice that's a bit mor economical is Sonia Kashuk's Lip and Cheek Tint($7.99 at Target stores). Be careful when using either of these, they're called stains for a reason. Also, be sure to start out with just a little bit (a dot or 2 on the apples of the cheeks) and blend quickly. You can always add more color if you want a deeper flush.
If you want subtle color that lasts, dab a bit of Benetint (or any other stain) onto your lips. This will be more of a rosy look. But if what you crave is true color that stays put all day long, your best bet is a long-wearing lipstick such as Cover Girl Outlast Double LipShine ($8) or American Beauty Super Plus 10-Hour Lipcolor ($16.50, though currently on sale for $13.20). These can be a bit drying on the lips, so keep the accompanying gloss (or your favorite gloss or balm) on hand for touch-ups. It may also help to put on some lip balm about 5-10 minutes before you apply the lip color.
To help your regular lipstick stay on better, find a lipliner that either matches your lipstick or your natural lip color and fill in your lips entirely with it. This will give your lipstick a little something to cling to. Then apply lipstick with a lip brush. Go for thin coatings of lipstick, and more of them, rather than slathering on a thicker coat. I've been impressed by Revlon ColorStay Soft & Smooth Lipcolor (approx $8 or $9 at drugstores) and MAC lipstick($14).