For better facial skin, should I wash with water only or use a face wash with ingredients like salicylic acid?

Water's fine. Warm water and if dirty, mild soap is all you usually need. Salicylic acid and its derivatives are keratolytics (agents which cut through skin cells and can thin the skin, reduce the size of calluses and the like). Skin normally sheds on its own--half of household dust is human skin!
Oily skin? If you have oily skin or are prone to blackheads or large pores salicylic acid is approriate. If however you have dry sensitive skin salicylic acid may be irritating, .
If you're oily. If you have oily skin, salicylic acid is great. It's a beta hydroxy acid that breaks apart dead skin cells and penetrates oil very well. For normal skin or as a daily wash it can be harsh and irritating. You can even develop an allergy to salicylic acid as it is a medication.

Related Questions

Would that be okay to use face wash containing salicylic acid in it for whiteheads prone skin?

Yes. Facial products containing salicylic acid are over-the-counter and sold in stores everywhere. They are often used to treat acne. Once a day face-washing with a salicylic acid product is ok, but washing too often or scrubbing too vigorously may lead to irritated, reddened facial skin. Acne is a hormonal problem that leads to certain bacteria growing in oil glands. Acne is not caused by dirty skin. Read more...

I am using neutrogena's acne free face wash with 2% salicylic acid. My face is okay with that but skin around my mouth becomes too dry. Why is that so?

Add A Moisturizer. Irritation, dryness, redness are frequent side-effects of many topical acne meds. It is important to use an oil & alcohol-free skin moisturizer twice daily after washing your face. Finding the right balance of medication can be challenging even with mild acne. Can also try using Sal. acid every other day. If irritation continues or acne not responding, see your doctor for tolerable treatment plan. Read more...