Well, it does have an amplifier but it's part of the brainbox (CDM) which controls the other stuff such as the clock. You'll find that above and to the right of the gas pedal. Something like three 7mm bolts hold it in place.
As for an upgrade? Check this thread out started by AK49BL:
https://www.gmt400.com/threads/88-94-factory-stereo-info.48716/
There's a lot of good info in there along with photos to help identify which units to hunt for. Essentially, if you want to keep the stock set up you'll need to hunt for a CDM from another equalizer equipped unit with the upgraded cooling fins. Pull that unit, cross reference it with AK49BL's list to check it's the right one and install in your truck. That's what I did and have found it adds a bit more oomph as well as ability to drive lower impedance speakers- the display doesn't dim nearly as much as the old CDM I had (My truck is also an '89). As for speakers? I highly recommend Infinity Kappa 64CX 4x6 plate speakers:
https://www.infinityspeakers.com/kappa-series/KAPPA+64CFX_.html?dwvar_KAPPA 64CFX___color=Black-USA-Current&cgid=kappa-series#start=1
You can find them cheaper elsewhere, but that's got accurate factory specs, one of the most important being sensitivity. At 94dB (1w/1m), that's the lowest I would go with a factory set-up. It'll be louder than you remember and will actually sound much, much better.