Many great advices here! One thing to consider is if you are familiar or not with running cables and wires and if not, I would stay away from the attic as it could well be the most tedious way to go about it as you have to go from basement all the way up and then back down in to your chosen wall. Also consider very seriously the advice of fishing only through inside walls as you do not want to alter insulation of the house while fishing.
Ron has mentioned CAT3 wire which is quite possible this is what your new house would be using. However, CAT3 is not twisted pair if I am correct but as Ron mentioned, for short distance it could do the job. JohnnyG has also mentioned a very good point as contractors will often run one cable paralleling from one outlet to the other as this is the most economical way for them to do this task.
One way to check this is by using a toner and sniffer. I do not know if you own such or maybe a friend or if you intend to do all kinds of other cable runs, this might justify the expense. I bought mine at Home Depot for less than 100$. That specific type (and most of them) have RJ11 male included on the toner which you simply plug in to one of your outlets and while tone is generated through the outlet, you simply go to each outlet and insert the tip of the sniffer while pressing the on switch (high or low).
If they ran the cable in parallel to each outlet, you will hear the tone. If you do not hear the tone in one outlet, do not take it for granted and check them all! If they are not in parallel, then you can use an Ethernet plate which will allow you to use for this purpose. Now, if the tone is all over your outlets, you will have to forget about it and use some alternate options.
As I pointed out, if you are not familiar with running cables you should use the simplest and shortest alternative which would be to choose the area where you want your connection(s) get a caddy clip (ask home depot they will know). Using the caddy clip to draw the hole in the wall at normal outlet level, you then use a small gypse saw.
In the basement, look at where you want to feed your cable. NEVER EVER leave cable loose as if you are to install a ceiling later on that cable might be at stake during future renovations. Therefore, what I would suggest you do, drill holes where ever necessary in the Joyce.
You must use a drill bit of approximately 4' and feed it through the hole in the gypse and once the hole is done, you leave the bit inside the hole and go back in the basement.
Now that all your holes are completed, start running your cable from your Ethernet panel through all the holes in the Joyce.
Now, you are ready to feed your cable to the upper floor. The end of the drill bit should have a small hole at the tip of the bit where you can feed a strand of wire from your cable through the hole. Fold the strand of wire over and using electrical tape, you would tape that piece of wire over the other wire, tape evenly, making it strong but make sure it is not too thick as it needs to go through the hole.
Now, while pulling back on the drill bit. Make sure the cable in the basement is neatly stretched so it is not tangled. If you have someone else downstairs to control it (box) is not a bad idea.
Now your next step is to install the caddy clip, your Ethernet connector and wall plate (make sure you choose a connector which includes the tool to secure the wires in place).
Now, if you don’t feel comfortable with doing this type of work, you may want to reconsider going wireless. Yes there is draw back but you are the one that knows the kind of use you will be doing with the service. When speed is not so much a factor, this is a viable option.
However, a strategic location must be chosen in order to be efficient. IE: My sister was loosing communications at times and I found out that where it was located was not the most efficient location. I told her to move the router closer to the stairs as that was allowing the RF to flow more evenly through the house.
RF will go through walls but there are limitations if you position the router strategically by doing some tests, it should be very effective. Look at all your options and what you really want then as Ron mentioned; give us another shot at helping you.