I've ordered from them a few times. No problems with the service.
Standard hookup wire has a standard number of strands and a PVC insulation. If you want more flexibility, you would need to find wire that uses a higher number of finer strands. It's out there, but it can be hard to find. You can also find stranded wire that has a rubber or rubberized vinyl insulation, but again, it can be hard to find.
Solid wire is solid wire, you might be able to find different insulation materials, but it's mainly PVC. The only real difference is if it's nickel plated or bare copper. It's better if it's nickel plated.
You can find test lead wire that has a flexible insulation and a high strand count, but it's expensive and bulky, probably not practical to use inside a mod.
If you're having issue with the flexiblity of your wire, you may want to consider using a finer guage. Wire as fine as 22 gauge has low enough resistance to carry several amps for the short distances inside a mod. 18 gauge is generally overkill for use inside a mod unless it's a long run.
For example 22 AWG has about 16 mOhms per foot so a run of 2 inches would be 2.6 mOhms. With a current of 5 amps that would be a power loss of 66 mWatts and a voltage drop of 13 mV. 18 AWG has about 6 mOhms per per foot so a run of 2 inches would be about 1 mOhm for a power loss of 25 mW and a voltage drop of 5 mV. There's just not a difference worth getting concerned over.