I'd like to get a couple GI style cleaning kits. Can anyone recommend a good source? I see them for less than $10 on ebay, but I have my doubts those are worth the pouch they come in. I bought a brownells version but, honestly it was a PITA to use, I felt, particularly the T handle that never cooperated.

Bore snake and  small bottle o CLP

A lot of the internet/Ebay stuff is made in China and often the threads are off.

You can buy the real deal from reputable companies like Fulton Armory.  You'll pay more but get real USGI kits.

https://www.fulton-armory.com/

Amhurst does/Did sell USGI kits.

https://www.amherst-depot.com/

Some of the better surplus sites should have them.

Fulton Armory once had a batch of NOS Colt cleaning kits. I picked up a couple and they are the best cleaning rods I ever used.

Aside from that I recommend picking up the Otis kit.

This is a good entry one: https://otisdefense.com/warrior-series-basic-weapons-cleaning-kit/

The one that I highly recommend is this one: https://otisdefense.com/i-mod-cleaning-kit-5-56mm/

That is actual USGI kit but sometimes you can get a surplus kit off midwayusa when they get them. I also seen the Deluxe clam shells being sold in surplus stores now and then.

https://whatacountry.com/colt-m16-cleaning-rod-and-brush-set.aspx

https://www.apexgunparts.com/colt-ar15-m16-cleaning-rod-and-brush-set.html.html

OP I have picked some USGI cleaning kits up from Midway USA and also Bushmaster over the years.  Just make sure you are getting something legit, made in the USA and not a weird thread pitch that needs some sort of an adaptor.  I always use USGI cleaning kits and have been for over 20 years now.  Ever seen one of those magical pull through cord type kits have the cord snap and the area containing the brushes get lodged in the barrel?  It's not cool.

Since I last posted, it appears Fulton Armory has their NOS Colt original USGI cleaning kits back in stock.

https://www.fulton-armory.com/cleaning-kit-original-colt-usgi-nos.aspx

These are seriously the best I have ever used since I bought this Kleenbore kit from abut 15 years ago. I still have the adapter to convert the threads to the 8x32 standard threads. They have a Proshot adapter for 4 bucks: https://www.midwayusa.com/product/1014845686/pro-shot-thread-adapter-8-x-36-military-to-8-x-32-standard-brass

I bought two of the converters for my t-handle so I can put in a standard thread chamber brush.