Today I wanted to fly and could take off from the runway of my choosing. I have wind from 040 at 13KT and the one runway is 09/27.
Which runway should I use?
I would use runway 09 because an aeroplane should start against the wind, but then I have crosswind, right?
Crosswinds are part of flying, airfields have a limited number of runways but wind can come from any direction, it's rare that wind is straight down the runway.
All airplanes have a demonstrated crosswind limit, determined by the characteristics of the airplane, pilots take that into account as well as runway conditions and their own proficiency when deciding how much crosswind they can tolerate. It's almost always advisable to take off into wind, with the lowest crosswind component, in your case there's only one into wind option which is 09. Winds of 040 at 13 knots would be 50 degrees off the runway, which equates to about 10 knots of crosswind, which it totally doable in any airplane you're likely to fly, with the exception of some tailwheel airplanes.
Better a crosswind with a headwind component, than a crosswind with a tailwind component!
Your only sensible option is runway 09 in the situation you have presented.
As the other answers have indicated, you want to take off into the wind as much as possible (aside from other considerations like runway slope or obstructions). The airplane has a maximum demonstrated crosswind component, but you also need to consider your personal minimums / maximums.
As GdD's answer indicates, this scenario has about 10 kt of crosswind, which is acceptable for most light airplanes. However, if you've always had a direct headwind, or only a few knots of crosswind, this may not be a good day to fly. Or you maybe need to grab a CFI and practice some landings with higher crosswinds than you've seen before.
Many pilots will (or should!) write down their personal mins / maxes, so as to better help adhere to them. Some examples of such mins / maxes might be:
Most of these criteria are more restrictive than the aviation regulations specify, but as a new / student pilot you don't have the experience to fly at minimums. And they mean that there will be days where you won't fly, even though there may be a full pattern at your airport.
As you gain experience and confidence, you will want to adjust your personal minimums - maybe once you've done 3 (good!) landings with a CFI in a crosswind of 8 kt, you increase your personal max crosswind component from 5 kt to 8 kt. If you haven't flown for some time, you may want to make your personal minimums more restrictive, too. These are not set in stone, and can (and should!) change as your experience, knowledge, confidence, and currency changes.
All else being equal, yes, you should takeoff into the wind as much as you can. However, depending on the airfield, there may be other factors such as terrain obstructions and runway slope that skew this decision.
With wind from 040, the ideal runway is 04—just drop the last zero.
However, most of the time you won’t be so lucky as to have an ideal runway available, which means dealing with some amount of crosswind.
Of the runways actually available at your airport, 09 is closer to 04 than 27 (on the compass or DG/HSI), so that is probably the better option.
Note that wind is just one factor; there may be other factors, such as terrain, traffic, ATC, length or surface that dictates using a different option. You should practice crosswind and tailwind landing with your instructor to be ready for those cases.
