Though since the Timex Sinclar 2068 was borrowed and easily confused (try nesting 5 for loops) I am not sure it really counts as my first home computer, especially since it could not connect to anything other that the tape player and cartridges I had.
The first one I bought was a Tandy Computer 2, with a multi-pack interface, dot matrix printer and an external dual floppy, used of course. OS/9 was a pretty cool compared to DOS and Deskmate was a neat interface. I used this to program, connect to BBS systems (where I met many people) and university computers at 300 baud. I had a basic word processor on this for papers, and handed it down to my parents who wrote an unpublished book on it.
The next one was a Tandy 1000 TL, a 286SX (that's right half the bus) with a blazing 1200 baud modem, 3.5 inch floppy and a 40 MB hard drive, monitor and a Dot Matrix Printer for $3500 new. I expanded the RAM to 786K to give video more space, and bought my first online purchase for this the 80287 math co-processor. Found a guy online selling them, I mailed him a check, he mailed me the chip. Real trust there. I used the modem to transfer the book off of the COCO2 to this computer and imported it into Word Perfect. Connected to the university computers to do coding assignments and play games, downloaded stuff as well as uploaded my first shareware (now freeware) to reset the Tandy Graphics to normal mode. Most third party developers did not know the assembly required to get out of Tandy graphics properly, so I got the system manual with all the details and created a program you could run in a batch after you exit programs like Fractint to reset the graphics, if you didn't reset, they were all weird when you opened something like Word Perfect. I wrote my own password based access system on this, preventing my roommate from playing games on the PC while I was at work and insisting he gets time to use it for homework when I got home. I sold this whole system online to a collector. He ended up playing for 90% of the shipping, I lost 10% of the shipping in the deal. Used 3.5 inch floppy to transfer my parent's book to a Windows PC and convert to Word, it is still unpublished, not for the lack of trying.