What gauge wire do I need for basement sub-panel?
Never, ever scrimp on a panel

When I hear "100A panel" I tend to think very small panel.  Don't get caught by that.  Spaces are cheap, and you want loads of extra spaces. Firstfor future expansion (it's frustrating not to be able to add a feature for lack of spaces). And second, when the inspector comes 'round and says "these circuits need AFCI".  My goal is to finish a project with less than 50% of spaces used (but without using double-stuff breakers).  A neat thing about panel pricing is you can get industrial tier panels like CH, QO, GE or Siemens for about the same price as tenant tier lines like Homeline or BR.

Wire size

In aluminum wire, you need 


60A: 4 AWG ($92)
80A: 2 AWG ($137)
100A: 1 AWG ($167)


There is a "100A bump" because circuits >=100A get to pull out of the 75C column in NEC Table 310.15B16 instead of the 60A column. However in your case the numbers don't quite line up; 2AWG is rated 75A@60C and 90A@75C. You can "round up" to the next breaker size, so 60C gives you 80A breaker.  Sadly, 90A breakers do exist, so you can't call it a 100A circuit (unless your AHJ agrees; worth asking since this is quite close and there's precedent).  

100' is below the 115' threshold where anyone even starts to care about voltage drop.  If you want to upgrade wire sizes to deal with voltage drop, that is fine, but feel free to upgrade breaker sizes also. 

I don't know what your total project cost is going to be.  Obviously if this all DIY the wire cost is a significant fraction, but this ignores the value of your time.  Contracted it's at least a $600-1000 job.  A small increment in wire costs can give you a lot of headroom in the future.   It'll even help with home resale value.