I am sorta in the same place you are, but several stumbles ahead on the path.
It is a good point ramseybuckeye makes, you are likely buying the lens for the 300mm end, and you will more than likely start to drool over even longer lenses the moment you get it.
Of the options above I would say they are steering you right in getting a used 55-300, they are sub $150 on ebay just at a glance and that's a handy range for a nature or even a city walk around lens to snipe people and whatnot.
That said if you plan to use a teleconverter to satisfy your inevitable urge to zoom more that this will create, you will eventually want something faster than a 55-300 due to TC light loss, which means more money. To go back up to ramseybuckeye's advice, you may want to look into long primes which are often faster can cost a fair amount more. It depends on whether this is just a long ranger sniper lens or if you want the zoom walkaround. Also remember teleconverters disable AF and any with the A contacts tend to be harder to find and can be expensive, I lucked out on the awesome one in my signature which most people have never heard of.
I had to have FF lenses so I can share them with my film cameras so I had to choose differently. Plus I am poor.
I can tell you the Tamron I have in my signature isn't very impressive but they are cheap.
I just bought one of these
SMC Pentax-FA 80-320mm F4.5-5.6 Reviews - FA Zoom Lenses - Pentax Lens Reviews & Lens Database for $29.81 shipped off ebay because it has paint fingerprints on it and is dirty (used by a painter) and was listed strangely, but I can see in the auction it has a UV filter, both lens caps and even the original box so its likely in perfect shape functionally. Hopefully its an improvement on the Tamron (which will be on the trader if this new one works).
In general I have found variable aperture zooms to be cheap in price and cheap in quality. Newer stuff is much better simply because of tech advancements.
EDIT: with a K10D you will really want to consider lens speed and the effect of a teleconverter. Lenses are less than ideal wide open, and with 5.8 aperture at 300mm that DA will probably have you at higher ISO setting a lot more which is something the K10D doesn't do as well as something like a K5. One of the reasons I plan to get a used K5 to replace my K20D actually. K10D with the last of the CCD sensors is really a wonderful camera though.