To Narrow down the specifics:

1. The software needs to be able to play a loop efficiently.
2. the software needs to be easy to use (to a degree; helpful online tutorials are a must)
3. the software must be anywhere from free to relatively cheap for one person to purchase.
4. (the two games planned are not going to be made immediately; the software does not necessarily need to be compatible with an engine or development tools and only needs to be good for prototyping the score)

In addition, these features are an absolute must for my purposes:

1. Access to obscure, ethnic/culturally traditional, and ancient reconstructed instrument sounds
2. the ability to play the score with a degree of decent sound

As for the type of music I wish to create:

1. the game represented by the first tag features what could be described as a "Gothic/modern Yuki Kajikura" vibe; it's score features a distinctly subdued gothic/modern combined edge, but mixes instruments and languages from many different cultures. the subdued, intense score represents the game's intricate plot and complex, plan-focused gameplay.
2. the game represented by the second tag is more conventional, featuring more techno/electronic tracks that are faster paced and more upbeat, yet suitably intense for the game's visceral story.

So, any suggestions as for what software could be used?

It sounds like you're talking about 3 different types of software.

First off you're looking for a DAW to create and edit music. There's a pinned article at the top called 15 good DAWs, read that one, it's lists a few good and cheap/free programs you can use like Reaper or FLStudio.

Second, implementation in game won't be from the DAW, that's going to be done within the game engine itself or audio middleware like FMOD or Wwise.

Lastly, virtual instruments are going to come in the form of a plugin that will work within your DAW. If you're looking for a wide variety of ethnic instruments that sound good (for free) you're out of luck. Your best bet will probably be SampleTank from IK Multimedia. It has a ton of instruments including many obscure ethnic ones, but the quality is not great. Runs about $350.

I would suggest just hiring a composer. Put a post in the classifieds sections, and if you can't pay upfront, just offer a profit sharing deal. I'm sure you'll find someone who already has the software/equipment, knows the ins and outs of the software, and has the skill to make what you're looking for.

The gist of this: Logic X, Audacity, and FMod.

The rest...

Agreeing w/ CCH about the functions of different applications. Think of it like working with Adobe products - you manipulate a photo in Photoshop, put it into a document with InDesign, create a logo with Illustrator, put the logo in a document with InDesign...applications serve different functions in a process.

Freeware DAWs are a lot better than you'd think, but if you're willing to drop a little money, Logic X from Apple is the best bang for your buck - pro editing capabilities, extensive libraries that may suit your needs regarding certain instruments (when downloading samples as you install, download all sound options). They can tide you over until you eventually purchase higher end orchestral libraries/samples.

A note on purchasing orchestra packages - you probably will have to buy two to really work with a "full" orchestra or set of specific sounds you're looking for. Some sets are ensembles, other sets feature more solo instruments, few really good libraries feature both. The best definitely don't. They're all pretty expensive if you're looking to keep your costs very low.

Google and YouTube Spitfire Albion and EastWest Strings, those will take you into the world of great sounding instruments. And look into downloading the free Kontakt 5 Player from Native Instruments in case you need it for your string/instrument library to work within your DAW.

Ultimately, I feel Logic X is the best option for you to get a solid DAW + some sounds you can begin working with right away. Its Sculpture plug-in can help you create or recreate sounds you may be wanting too.

You'll very likely need to get your final sound files into .ogg - Audacity can do that as well as other things that can help you work with your tracks. Older Fmod Designer (it's Studio now) tutorials illustrate that in adaptive music tutorials.

To get things looped and to create adaptive music, FMod's the way to go (from how I understand your project - Elias could also work) I reccomend Fmod because the FMod YouTube channel has a wealth of very clear tutorials on how to make that work, and as long as you're working within the realm of their free-to-use license, you're keeping costs down while working w/ industry standard stuff.