Do the TW, THW and THHN or THWN wire insulation types matter in terms of powering RAMPS 1.4 or the MK2a Heat Bed? I'm still looking at wires for my Prusa i3, to go between the power supply and RAMPS 1.4, and the power supply and the MK2a Heatbed.  

I also recently found a 400 ft. Wire Storehouse that I bought from Harbor Freight which has wire sizes in it from AWG 10 through AWG 22 (and additionally speaker wire, Zip Cord and Bell).

I also bought some reading material, I picked up Wiring Simplified 44th edition, and in it on page 28, Table 4-1, there is a table with information about the Ampacity of copper wires including their maximum temp (C), and maximum carrying current (Amps) based on their insulation types.

Unfortunately, the 400 ft. Wire Storehouse does not provide any information in regards to the insulation type or quality and this makes it difficult for one to choose the correct wire based on the specification in the table.  

Given that the thing only cost $30 for 400 Ft. of wire, it would lead me to believe that the cheapest grade of insulation was used; as I understand it, the TW type wire.   

I also read a forum somewhere in which people were complaining about the cheapness of the wire in this kit, stating that one ought to wear gloves when working with it as there is probably lead in the insulation as well as the wire.

The largest copper wire I have found in the table that I have (AWG 10) says that it is rated at 30 AMP regardless of which type of insulation it has, should I be using the speakerwire instead?  That isn't listed in the table.  Also it should be noted that though the ratings for the Ampacity are 30 AMPs, the max temperatures are different; with the TW being at 60 C.  

As far as I can tell if I use the AWG 10 (TW?) to connect everything it won't matter, but I just thought I'd check here to be sure first since my power supply is rated at 30 AMPs and that's probably the same as the wire....
THHN wire is thermoplastic high heat-resistant nylon coated wire.
THWN is thermoplastic heat- and moisture-resistant nylon coated wire.

"T" stands for thermoplastic insulation covering the wire itself.
"H" stands for a heat resistance of the insulation max 167°F.
"HH" stands for a heat resistance, but increased max 194°F.
"W" is for moisture resistant.
"N" is for a nylon coating make the insulation oil and gas resistant.

In my opinion the Wire Storehouse is good for simple stuff, but I would not use it for something I consider important.   It's quality is poor on the insulation rating and the number of strands is low.  Higher strands number allows for more flexible wire.

If you get high end audiophile type speaker wire it could be considered as you can find high strand number with good quality insulation properties in heavier gauges. 

Or your local auto parts store will carry 8 and 6 gauge wire with better insulation properties.