The old system was an original black and silver console, speech synthesizer, and a cassette deck. I stuck with that setup for a while, eventually getting a Mini-Memory cartridge and learning assembly programming on that. The fully expanded system included a peripheral expansion box (PE box) with a modified fan. (I kept the beast in the bedroom, worked at it late at night, and I had to keep it quiet.) The PE box held a standard 32K memory card, standard RS232 card, and a CorComp floppy controller and two half-height DSDD capable 5 1/4" Shugart drives. The console eventually held an 80K Gram Kracker (an exotic device described very well here.) The printer was a rock-solid Okidata Microline 92, the joysticks some Atari clone joysticks I can't really remember which had to be connected through an adapter I still have, and a continuing succession of modems that went from 300 baud up to a speedy 2400 baud. (Never did have or use the acoustic coupler.) My first display was my TV, but I soon graduated to a small but excellent 7" TV/monitor with AV inputs, and finally graduated to the Panasonic branded version of the 10" color monitor. I still own the 7" TV/monitor and the Panasonic, and both still work.
These days I'm using 3 1/2" diskettes and some venerable 5 1/4" drives, as well as a new CF drive attachment, attached to a range of hardware in configurations that can and do change according to what I'm up to. In most configurations they're better systems than the one I sold, although, of course, one can still do next to nothing with it that's actually productive. But it's about fun, not productivity. In any case, below are the three most typical configurations I use these days.
This is a 'working' system, but it's down in the basement so not often in use. I don't use the Gram Kracker in it because it doesn't play nicely with the P-Gram+ card. That means that I loose some the custom modifications I made to the TI's 'OS' through the GK, including my beloved modified character set. Nevertheless, the P-Gram+ provides the ability to load modified cartridges, like my ultimate modified Extended BASIC, and it has four banks of GROM/GRAM space instead of only one.
The RAM disk card is a nice addition because of it's ability to run a boot-up menu and hold some key utilities in battery-backed RAM, but it's old and the connections to it's NiMH rechargeable batteries are not so good. I like it, though, and maybe someday will get it a lithium battery upgrade.

This main system is shown with my basement 'museum/data center' and has easy access to serial ports on multiple old systems. Also in the picture is my oldest system: a '386 based tower in which I've installed 5 1/4" And use with the TI99-PC program.
This unit usually includes my Gram Kracker (alas I only own one,) a speech synthesizer, and the new CF7A+ system with 32K memory and a parallel port. The CF7A+, hand built one at a time by Jaime Malilong, emulates memory expansion, adds a parallel port for printing, and provides 'disk access' to diskette image files which are in turn stored on a handy CF card. No floppies. Just for the sake of demonstration, it's shown below with a newly acquired flat-screen 7" TV/monitor which has the wrong aspect ratio, but what the heck. This system is usually kept in the little sunroom next to my home office, and since the CF device is new I play with it quite a bit, trying to assess the pros and cons of images vs. diskettes. To print I have a solid old Citizen's 9-pin.
(I finally located and purchased an Okidata Microline 92, but I'm having trouble with the interface. If it ever works it will join the ranks as an alternative print device by the second half of 2008.)

Along the line I also acquired a CorComp 9900 Micro Expansion system, another device I had always coveted. The 9900 includes 32Kb memory expansion, RS232s ports and a (real) diskette controller all in one little box. I use the 9900 with a spare console and an external enclosure holding a 5.25" and a 3.5" disk drive. The GK in combination with the 9900 is the closest match for my original system, and much quieter and more compact. I plan to move this system around, and can switch the little monitor and/or either working printer from the CF system to this whenever I have to deal with 'real' diskettes.
I can set it up on my desk, plug the display output into A/V ports on my big monitor and view it on a PIP screen. I can also plug the RS232 output (through a USB adapter) into my PC for data capture or file transfer, or plug he display into my WinTV device for recording the audio/video output.

It's shown here on my desk with a PIP display in the upper right of my main monitor and an RS232 output to my PC.
And there's also a console I keep in my summer house just for games,

shown here attached to an old 5" TV/Monitor/8mm VCR (no, I never throw anything away) and with one of my Epyx 500XJ joysticks for 'serious' game-playing. I keep the other Epyx at home along with some TI joysticks, and yes, I still own a cassette recorder and the dual cassette cable. Don't use 'em, though.
I'd like another 80K Gram-Kracker, because I hate to keep moving the device between systems. If it breaks, I'm doomed. I'd also like one more speech synthesizer, just for completeness.
It'd be nice to get my Okidata 92 working with the right cable or whatever it needs, and if I did that it would be nice to have a tractor feed for it. And given the nature of the device, a spare print-head would be wise. (Ouch! I remember they were quite expensive and tended to go bad. I think I went through 3 of them on my original system.)
A hard drive controller and RLL drive for my expansion box would be nice, although I understand they're very cranky and also may not be compatible with my CorComp floppy controller. So I suppose I could use a second expansion box. (Gee, I just sold one just last year...)
I probably will buy another CF device, especially if Jaime or someone adds a serial port option.