I'm running Mavericks on my 1,1, although there's no technical reason why I couldn't run El Capitan. Sierra is the end of the line for them-the CPUs don't support the instructions.
In any case, I've made the following upgrades:
1. 1gb 8800GT from MacVidCards. Upgraded video cards are necessary for newer OSs, and in 10.7 and newer you don't need to use a flashed video card. With that said, I opted for a bit of "luxury" to get boot screens
2. Kingston 256gb SSD. I should have spent a bit more on the SSD for a work computer, but this works fine and the SATA bus is slow enough that it won't benefit from a high end SSD(like the 850 EVO in my main MBP). It's quite snappy
3. 16gb of RAM. With 8 RAM slots, this is cheap to do these days and you can put in a LOT more if you want to. The RAM runs VERY hot in these, and it is recommended that you use Mac Pro specific RAM that has very large heatsinks. With 8x2gb sticks with the MP heatsinks, my RAM is usually in the 70-80ºC range. With that said, the RAM is registered DDR-2 which is widely available and inexpensive as servers are its main application. Almost all you will find has some sort of heat spreader, and many folks are running plain registered RAM with the standard heat spreader style.
4. Upgraded to dual x5355 CPUs to get 8 physical cores. This requires flashing the firmware to MP 2,1(there's a utility to do this). Truthfully, there's not much advantage in doing this for most purposes, but this is an inexpensive upgrade($30-40 for a matched pair on Ebay). This really is a lateral move from the stock x5150s as the clock speed and cache amount is the same. x5365s bump you to 3.0ghz which cost a lot more.
One of these days, I'm going to put in a RAID card and run some of the 15K SAS drives I have. This is really not a practical upgrade-I'm mostly doing it because I have the drives-but will be interesting. I actually bought a RAID card but unfortunately it was for a Mac Pro 4,1 or 5,1.
Oh, by the way, I can't forget the dual aluminum 23"s, Magic Mouse, and Unicomp Spacesaver M. I feel like I'm in my "command center" when I'm at that computer. I'm just glad I have an office to myself with that keyboard