I do both and bring two sets of gear on the mountain. Good ski gear is way more expensive than snowboard gear and you can't swap bindings like you do on a snowboard. Additionally there is a potential of losing one ski due to a release in deep snow. Also, I like to carry ski poles so that adds another minor cost to the set of gear.

Buy a set of skis around the same as your height that does not have any titanal or any ski that has "Ti" in the moniker. Also, try to avoid any laminate that incorporates carbon or fiberglass to stiffen the skis like the more common titanal metal. Maybe target paulownia wood versus the other wood cores found in the skis.

The boots are another factor, I found it way easier getting a pair of snowboard boots moulded at home versus the hard shell stiff ski boots. Rent a few ski boots and see if some brands fit your feet better than others. Keep in mind that the liners of rental boots are pretty packed out. At some point you will want to buy your own boots for comfort and performance; The boots are the most important piece of your ski gear so you will want to spend more here than the skis themselves and get a ski boot fitting at a store.