If I were starting out and wanted to make my first golf club investment, I'd buy the IRONS. Sure, you will grab your putter on every hole. But, you're going to swing an iron on every hole too. There are lots of deals available on last years models. Do take the time to get fit at a local golf store. That doesn't obligate you to purchase anything, but find out if your swing requires an upright or toe-down lie angle. If you are standard, then you can get away with "off the rack" clubs. At that point, hit everything and expand your considerations to ALL the club manufacturers. Also, choose a make-up of clubs that fits your skill level. Trying to hit 3 & 4 irons as a 33 handicap will make for a long day. Consider driving irons and or hybrid's for the longer clubs. Adam's may be a good club choice.
Also, think about your wedges. Another personal item. Will you add matching wedges to your new irons? Do you like the wedges you currently have? You probably pull out your wedges on every hole too, so think about getting wedges that you feel extremely comfortable with.
Not to place the putter at the bottom of the list, but any putter will knock the ball in the hole. For the money you will spend on an Edel, you can get several swing lessons that will go farther in improving your score than a custom fit putter. Before I had an Edel, I thought I was a good putter and made lots of putts per round. It was threads here that got Edel into my head. I'm poorer for it! There is science behind the fitting process, but players were getting it done before this was introduced. Get a putter you like and master it before taking the leap to an Edel.
Hope this helps. Happy shopping!