Whatever wire you use, if it's going into construction, make sure it is rated for the purpose. The most common misuse I've seen is lack of FT4 rating.. I'm not going to list every type of suitable wire because it would be rather long and time consuming, especially if you're willing to run conduit.
For LVDC voltage controlled LEDs, I'm personally partial to Securex cable (Commonly used as fire alarm, doorbell or security wire). From experience, always check similar types and the cost of the next size or two up as sometimes a more common wire type of the same size or more common size of the same type is cheaper. Securex is excessive to the ratings you actually need, but it's very common so it's cheap for what you get. If the hardware store doesn't have a suitable FT4 rated, preferably stranded cable, call around to the electrical wholesalers in the area. Some types of extension cord wire can be suitable as well.
Low Voltage DC Lighting is particularly sensitive to voltage drop because of the high current per Watt, so it's best to actually calculate your voltage drop as it's rather easy. EE Stack Exchange has numerous questions regarding use of these LED strips by the way and you might want to read the canonical choosing a power supply question. Find the resistance per meter/foot for your wire size, multiply by the length to find resistance, and multiply the resistance by your anticipated current to get voltage drop. Try to keep it to only 1-2% of your 12V.
If you don't know how to calculate anticipated current, take the Watt/meter rating of your strip and multiply that by strip length to find wattage. Divide wattage by voltage to find current.
The conductors built into these strips are rather small, so for best results, you should feed positive to one end and negative to the other end of the strip. This shares the voltage drop evenly between the LEDs instead of having a high current at only one end of the strip. For long strips, instead plan to run a wire in parallel and tap it in every 3 to 4 feet.
If a phone call doesn't bother you, don't be afraid to call a few electrical wholesalers. They like selling things and they're used to doing price checks on the phone so it's not like a big box hardware store where you have to wait for the guy to walk a block to the phone. Variance in price can be huge so it can be worth calling around and pricing things out. Lastly, if you are using any significant amount of wire, check the price of a whole roll!. If you need more than the largest roll from the big box hardware store, call the wholesalers and check the price of a larger roll!. For common 14/2 NMD90, where I live it's 70 currency for 30m or 95-110 currency for 75m. A potential cost difference of 84%! It's also worth checking kijiji or whatever local buy and sell boards you have for people getting rid of leftover construction supplies, and if you can find sufficient quantity of an acceptable cable, this is usually cheapest but you have to be diligent about checking the cable type and uses. Just read the jacket of the cable and look up its ratings.
One final piece of advice, if you can't get stranded cable, it is not impossible to use solid for the bulk of the wiring, but it may result in some extra precautions like bending a spiral spring into the wire where you solder to a strip so that the solid wire can't pull with significant force on the contacts, or using insulated butt splices to switch to a short length of stranded wire before connecting to the LED strip. This may allow you to get a better wire size at the same cost.
