A good moisturiser should leave your skin soft and glowing.
Moisturisers should not sink in so quickly that you hardly have enough time to massage them in. You skin needs a couple of minutes to allow your skin to absorb the product. It should offer you protection from the environment and keep your skin nourished and hydrated all day.
If your skin feels tight, dry or over greasy after 5 minutes of applying your moisturiser then it is likely that it is the wrong one for you.
A daily moisturiser should have an SPF of around 8. Should you be in the sun a lot then you might consider applying a further SPF on top of your moisturiser to protect your skin from harmful UV rays and premature ageing.