What is considered a "shorter length", "longer run" and what is "fixed position"? Do you believe they mean a straight line or is it something else?
A shorter length would be a patch cable running from a wall outlet to a PC or from patch panel to switch.
The term "fixed position" doesn't apply only to cable inside conduit. If only there were always conduit available!!!! However, that's not always the case....especially in a home environment. Fixed position really means, a cable that will not be moved. Generally, this applies to anything that goes from a patch panel to a wall outlet. Whether run through conduit or not is irrelevant. The point being, once it's been run, punched and tested, you will not ever be moving it again unless you remove and replace it at some point in the future.
With regard to braided and solid core cabling:
Braided (better known as "stranded" cable) is multiple small copper wires twisted together. Solid core is just that, the the wires inside the cable is are solid piece of copper wire.
In my experience, and I am a network technician by trade and have pulled and punched (and tested) more miles of cabling than I care to think about, neither one is any "better" than the other. Solid core is generally used for "fixed position" cabling and stranded for patch cables.
Your best bet is most definately to pull the wire to outlets. This will require faceplates and "keystones" (the RJ-45 ends that snap into the faceplate) as well as a patch panel for the other end.
If you want a good price on cabling, don't go to Lowes, or Home depot, or WalMart or Future Shop or any PC store. Call a company (or several and get quotes) that supplies electrical cabling. If you're going to do it right (ie: patch panel to outlets through the walls and ceiling space) you will first want to figure out how many cables you'll be pulling to the outlets. In the above reply, Arin stated he pulled 3 per outlet (2 data, 1 VoIP). I recommend you get 3 boxes of cable in a case like that so you only have to pull to each outlet once. Three cables at one time makes more sense, and is easier and less time consuming, than 1 cable 3 times. However, you're likely to end up with a lot of leftover considering boxes of cabling come in 1000 foot rolls.
Don't forget to test after running your cables. Those cheap little testers that have nothing more to them than blinking lights are the next best thing to useless. Get a professional quality tester that will also certify. You could likely call an electrician and have them come test for you a lot cheaper than buying a tester.