Transition to crib

Hi all, first time mommy and SAHM. I currently have our 3 month daughter sleeping in a rock and play in our room. I would like to start to transition her to her own room and her crib but am not sure the best way to do that. I have the pack and play set up in our living room thinking that would get her used to sleeping flat. She has Reflux and is on meds and doing wonderful. I have a wedge to put under the mattress but she seems to wiggle hwr way down to the bottom. I am just looking for some advice on the best way to do this. Cry it out, no cry or aome other method. She has recently started waking up as soon as I try to put her in the pack and play for her nap, she sleeps fine in my arms or her swing, even if they aren't moving.