Babies being babies means that as a parent you should get used to seeing red marks, scratches, little pimples (acne), rashes, and even bumps on your baby's skin. Because your baby's skin is so sensitive it is also susceptible to a whole range of markings but, for the most part, this is perfectly normal. Obviously keep a close eye on any markings that appear unusual or persistent and call your doctor if you suspect anything out of the ordinary, or even if you are simply unsure. Never let the Internet or a book be a substitute for medical advice if you suspect anything with regards to your baby (or yourself for that matter).
Generally speaking, a baby's skin will take care of itself so there is no need to be constantly rubbing oils and lotions into your baby. There are some instances where preventative skin care is worthwhile (such as using Vaseline to prevent rashes), but by and large you don't need a whole bathroom full of baby skin care products - no matter what the advertising says.
When you do buy products to use on your baby's skin remember that there are many versions of products that adults normally use (shampoo's, soaps, oils, detergents etc.) have a version that is especially formulated for babies and infants. These products are generally much milder than their adult counterparts, and are safe for use on your baby's skin (although you should always take time to read the list of ingredients and any other small print on the labels). Before trying out a new product however, it is often suggested that you first apply a small dab of the product on a tiny area of your baby's skin to check to see if there is any reaction of the skin to the product (behind the ear, on the wrist or on the top of the foot are some of the recommended areas). Remember to allow a period of time for any reaction to appear before using the product fully on your baby. If a reaction does occur, wipe off the product as best you can with water and take a note of the ingredients in the product. It is more likely that your baby's skin is reacting to a particular ingredient rather than the entire product, so you will need to keep an eye out for that with other products that you try. Again, your doctor should be able to offer good, impartial advice when it comes to what baby products you should use.
[For more than 900 baby health related tips make sure you pick up a FREE copy of The Mommy MD Guides Audiobook (while the offer lasts). Details here.]