If foundation ordinarily makes your skin feel thick and oily, then you're not using the right kind (the longer-lasting foundations are heavier as are the foundations that transform into powders so avoid these). In fact, you can pretty much avoid almost all foundations and stick to cream cover-ups and correction sticks for skin irritations and dark circles. Apply these and blend them by massaging them into the skin.
After applying a light foundation or some type of cover-up to the problem areas apply a thin coat of loose powder with a clean brush. A loose powder is delicate and translucent so it won't give you a “cakey” appearance. In addition, loose powder is easy to brush off any excess powder will blend easily and reduce shine. Only apply colors that don't look overdone and thick and pick shades that closely match your skin hue.