A lot of people are telling you not to buy skis. I think depending on how often you plan to ski it is completely worth it even for a beginner You can get setups for very cheap. My current park skis cost me $200 with $100 bindings, and my pow setup I bought used with skis and bindings for only $100. It's maybe $50 to rent so that pays for itself very quickly.
You are looking for an all-mountain ski, and there are plenty available. The main questions you want to ask yourself are what flexibility do you want and will you be riding deep powder. Softer skis are more fun and have more pop, but stiffer skis are more stable at speed and generally better for an all-mountain experience. As for powder, it really depends where you ski. If the mountain gets deep powder fairly regularly you will probably ride it. If powder is a concern then a slightly fatter waist ski with all rocker or rocker-camber-rocker would be ideal. Something like the K2 Kung Fujas. If you won't be riding powder then you don't really need rocker and all camber should be perfect for your needs. If possible try to demo both before buying though, because you might prefer one over the other. I like my all-around groomer whatever skis to still be rocker, because personally I just think rocker is a lot of fun even though it's technically worse for holding an edge on groomers. If you can't demo though I would lean more towards camber. It's more traditional and probably easier to learn on.
You are a lot shorter than me so it is hard to recommend dimensions, fwiw I ride 181 or longer at 6'2. Your shorter skis are more maneuverable and lighter, but longer skis are more stable, faster, and sort of smoother in the air doing spins because of something called swing weight. Whatever is recommended by like a size chart should be good for you, normally I would recommend going a bit longer but since you are a beginner it should be good. If you do go with rocker keep in mind that they will feel shorter than they actually are, because the running length is shorter due to the tips not contacting the snow.
For purchasing definitely check out [Evogear outlet](ww.evo.com/outlet/default.aspx). There are some great deals here, the skis are all brand new but they are leftovers from past seasons. So it will be the model from a year or two ago, but they are still brand new just leftovers that didn't get sold. To go really cheap you can try to buy used from Newschoolers or other forums.
Welcome to skiing, I agree about the maneuverability being better than snowboards. It makes sense, you have twice as many edges.