If you haven't been around for the qualifying offer discussions in the past, let's go over what will go on now. Samardzija is now able to negotiate with any team. In return, if he signs with another team before the 2016 amateur draft, a very likely scenario, the Sox will get a compensation pick between the first and second round of the draft. The team signing Samardzija will give up their first available pick in the draft.
With that bit of news done, the White Sox are now a week from the deadline for setting the 40-man roster in advance of the Rule 5 draft. The Sox have typically gone into the Winter Meetings, which start December 7, with a couple spots open. With the 40-man roster currently at 34, they can probably add four to the roster with more than enough room for any additional transactions.
The next deadline after that is on Decemeber 2, when the Sox must tender contracts to all the pre-arbitration and arbitration eligible players. The Sox have thrown a wildcard in here the past few years by non-tendering players who weren't up for arbitration. This happened to Dylan Axelrod in 2013 and Scott Carroll in 2014.