Please do not take this the wrong way, but in what you wrote, you had mentioned that you were new to handloading. Welcome into the fold, but when you bought your gear and set things up...did you even bother to read the introductory parts of the loading manual?
I am suspecting that you merrily bought all this gear, including new brass for your 223...right? Are you doing the same with new 308 brass or was the brass given to you (as fired)?
The bullets would have seated in...albeit, likely not very well because quite a bit of that new brass is not exactly round at the neck. I always run them through my resizer and then de-burr first before seating a bullet. It saves on mangled cases when trying to seat those flat base bullets.
Now to the matter at hand. EVERY reloading manual has an introductory section on the principals of reloading and (Hornady and Sierra) have excellent step by step procedures from the start to finish.
Do not EVER skip a step. The results could be injurious to your heath and your rifle.
As stated before, every fired case in required to be resized. The part I am confused about is how in the devil did you think you could seat a bullet in an fired case? The resizer die also removes the primer. Before putting a bullet in, you have to have the seated the primer, de-burred the case and added the correct amount of powder already as a minimum.
I suggest doing some reading before hand, otherwise, sell your reloading gear and just buy the ammo because you are a likely candidate to getting hurt.