The Parker (I had one) is a replaceable blade razor so the blade feels different than a straight. Also the cutting area is narrower, and you do not strop this one, just change the blade. It helped me learn some of the moves, but nothing like a straight.
My first blade was a Dovo Best Quality from Straight Razor Designs. I recommend a professionally honed blade like this for your first one. SRD also gives you a free honing when you buy a straight. If you want something more economical Whipped Dog Straights has the sight unseen deal, a shave ready vintage blade. The service is great. When you buy the straight, I recommend get a strop also. Theres a lot of information in this site it helped me a lot so browse every day and you always learn.