Yes you do need to chamfer the case mouth of new cases. Buy a vld reamer as many of the best new bullets need it. I trim and chamfer all new cases to a uniform lenght and deburr the flash hole. After you have sized , trimmed , chamfered and deburred you should weight sort the brass. Recent winchester brass has been terrible so avoid it. Three out of 50 of the last bag wouldn't fit in the shell holder and almost all had oval primer flash holes.
Hunthard, glad you got your problem worked out. Reloading is like fly-fshing, a whole lot of little details that all add up in the end. You've gotten some good advice here and as you get more experience you'll learn to take it for what it is (one person's opinion). For example, I don't agree with a lot of the post I quoted above. I use Winchester brass all the time, I've gotten bad batches of a few different brands but that doesn't mean they're to be avoided. Likewise, I don't believe new brass needs to be sized, trimmed and chamfered before the first firing, and you only need a vld chamfering tool if you're shooting vld bullets.
Sizing work-hardens brass which is a bad thing, so it's something you want to minimize. There's no need to do anything with new brass other than run it up in your sizing die just enough so that the expander ball goes into the neck to round out any dings. I wait until after my brass is fired once to trim and chamfer the necks; that way I can account for any increase in length that happens with the first firing before I trim it back to the "trim-to" length. I don't de-burr flash holes (the decapping rod takes care of any major burrs) and I don't weight-sort my brass, and a few of my rifles are honest 1/2 MOA shooters. I do measure runout and toss cases that don't seat straight bullets, but that's not something you need to worry about when you're just getting started.
Once your brass is fired, it expands to fit your rifle's chamber. You want to adjust your die so that the body and shoulder of the case is sized as little as possible to avoid working your brass; really the only part you need to size is the neck so you may want to look into neck-sizing dies rather than full-length dies. If you re-load for any length of time you may end up there anyway.
Again, this is just one man's opinion, so take it for what it's worth.