However, how you clean your face is becoming gradually more important (hello, double cleansing,) and with it so is the cleanser you use. You don't want anything that will totally strip your skin of all moisture and oil, but you also don't want anything that will leave behind the kind of day-to-day gunk that clogs your pores. If you wear makeup, you should take it off before you cleanse your face with an expensive cleanser. Period.
Outright, you should know that you can get a decent enough basic cleanser at the drugstore for just under $10. Drugstore brands like Purpose, Pond's, Dove, Eucerin, and Neutrogena are excellent. If you want to save money, save on your cleansers and splurge on high-quality foundations and moisturizers. Why? Something that stays on your face for just a couple minutes before it's washed down the drain is not worth spending as much money on as something that stays on your face all day.
That said, when you fall in love with a product, it's hard to let go, price tag be damned. A great example of a wash with a totally-worth-the-splurge price tag is RéVive's Foaming Cleanser, which costs around $75. It lasts a long time, smells amazing, and you know that it's doing its job well. If you have particularly finicky skin and find a cleanser that works for you, don't question it. It can take people years and hundreds upon hundreds of dollars to find a cleanser that works not only for the amount of oil they have, but the sensitivity of their skin.
Certainly, in skin care, there are products much more worth splurging on. You should spend money on pimple medication, soothing and clarifying masks, and prescription creams such as Retin-A micro. But when it comes to cleansers, a basic drugstore buy will get the job done; it'll remove dirt and makeup without stripping skin too much of its natural oils. However, if you're intense about your skincare, it might not get the job done as well as you want it to.
The secret to purchasing the best cleanser is absolutely to buy for your skin type. If you have dry or combination skin, stick to a low-weight cleanser like Farmacy's Clean Bee. It can be oily, creamy, or just thin. Try to avoid anything with alcohol in it, however, because it can dry your skin out. For oily skin, look for a gel formula like Peach & Lily's Powercalm. If your skin is particularly problematic, a lightly-exfoliating cleanser can do wonders. Make sure, though, that it's a chemical exfoliant and you don't overuse it, because scrubbing your face to no abandon will only irritate it more.