I had to look up TI-99/4A. Are there still TV sets today you could connect this to?
New TVs often don’t have analogue inputs, so you’d need some sort of analogue to HDMI scaler, which range from aliexpress tat to expensive enthusiast stuff like Retrotinks, with various hobbyist stuff like OSSC in between as well. Some really old stuff is RF only, so you might need a tuner as well (or an old VCR) to go from RF to baseband composite.
Older LCDs will probably have RCA inputs though they might not work with all retro computing stuff as the signals are sometimes rather “non standard” (not sure about this particular case).
CRT TV should be fine, as they’re from the right era and a bit less fussy about signals.
IIRC it just outputs video as a composite signal over RCA, so any TV with composite inputs (yellow/red/white) should be able to display it. Those are getting rarer I suppose but are generally still around, and most CRTs have them.
Use a balun and just hook it up to where you usually connect the rabbit ears.
The computer includes an RF modulator, so you need a TV that can tune NTSC channel 3 or 4.
Or, buy a DIN plug and make a cable that brings out the composite signal: https://99er.net/TIvideoadapter.htm
I haven't bought a new TV recently, but there seems to be no shortage of composite inputs on the sets I've been using.