Taking care of the delicate eye area is important in order to prevent the signs of ageing.
The skin around the eyes is fragile and often shows signs of ageing first before any of the other facial areas, so I would advise using a preventative eye care treatment from as early as your twenties.
As most of the damage is caused by UV rays & environmental stresses, in your twenties when applying your vitamin C in the morning, I would recommended to apply it around the eye area as well (as long as there is no irritation). Don't forget to follow with a broad spectrum high SPF eye sunscreen or mineral sunscreen.
In your thirties you tend to start to see the first visible signs of ageing begin to appear. I would start using an eye cream daily or even twice daily to help keep the skin elastic and prevent collagen loss around the eye.
I wouldn't advise using a regular moisturiser around your eye area. The skin around your eyes is much thinner, so it is prone to irritation and may cause milia around the eye area from using rich moisturising creams. Facial products, especially cosmeceuticals are formulated well and contain strong active ingredients to target specific concerns, so would be too potent for the eye area. I think that when you are in your thirties, you are more likely to have specific eye area concerns like dark circles, fine lines and puffiness that would require eye products specially formulated with ingredients to target those concerns.
That's why it is so important to use the correct eye product.
If you have puffy skin around the eyes, use an eye cream that contains caffeine which allows a temporary de-puffing by constricting blood vessels in the area.
For dark circles go for an eye product which contains ingredients such as vitamin C, licorice, Kojic acid, Chromabright or niacinamide which inhibit melanin production.
Make sure the retinol products are formulated just for the eye area.
The more that any of the anti-ageing ingredients mentioned above are included in your eye creams the better.
If the eye area is sagging/baggy I am afraid an eye cream cannot help. Only surgery will help remove that excess skin.
It is vital that you protect your skin daily against the sun. This also applies to the skin around the eyes. The problems of wrinkles, dark circles, etc. will only get worse if you go out without sun protection. Use either an eye SPF sunscreen or a mineral SPF sunscreen or make sure that your concealer is a minimum of SPF30 or higher. And lastly don't forget to wear sun glasses.
The most important thing to remember when choosing your eye cream is to make sure it is well formulated. That means choosing a cosmeceuticals brand that uses evidence based ingredients with enough active ingredients to target these issues. Most cosmeceuticals products are backed by science and not marketing rubbish. Remember that high street brands and department skincare products do not contain enough ingredients to have a noticable effect on the skin.