If you plan to do any kind of stuff in a DAW, I highly recommend doing so! You can have it for $49 right now as a registered hardware user (as long as the hardware hasn't been used for a discount before).
Yes.
Reaper would be inexpensive (plus it's coming with a literally never ending trial period), but in case you're familiar with the Cubase family already, I'd possibly try to get a cheap (or even free) smaller OEM version (some people are selling these).
In case you're on a Mac, get Garageband, which is free.
As far as Match EQs go, Reaper has one for free in their file repository somewhere, but in general, I wouldn't recommend reaper too much for starters.
Some bigger DAWs have a Match EQ coming with them, but those versions are generally more expensive and sometimes tougher to get into. Personally, I'm using Logic - but as Garageband, it requires a Mac.
I'd possibly start with a DAW that is easy to get into (such as Cubasis) and a set of analyzers (there's some free ones such as Span from Voxengo), then do the matching yourself - which will possibly even teach you a whole lot about the HX EQs.