It can be done and many marine aquariums have been maintained successfully without the employment of a skimmer. Having said this however, if you are a newbie, I would refrain from setting up a tank without a skimmer as it erases one of your safety nets and makes your testing and water parameter issues that much more important to optimize and harder to do.
This would require, frequent water changes and testing, limited feeding, increases biological and chemical filtration.
Don't get me wrong...you could do it! I am not using a protein skimmer on my 14 gallon bio cube housing Acropora, clams, porites, zoanthids, two damsel fish, Purple Lobster, Pistol Shrimp, sea stars, Electric Orange and Blue Hermits and snails with no problems.
Their are many excellent skimmers on the market that would be suitable for you size tank and not very expensive such as Bubble Mag and Aqua C EV models.