I bought an A1500 to replace my A2000 when it's PSU caught fire (long story). I upgraded the A1500 with a SCSI HD/2MB RAM Card, a kickstart ROM splitter that would swich between KS1.3 and KS2.0 whenever I reset via the keyboard, a Zorro RAM board and a Zorro Scan Doubler/Flicker Fixer.
If you're thinking of installing a hard drive then I recommend the Buddha Gold IDE Zorro card that will let you connect 3.5" and 2.5" Hard Drives, CD ROMS, etc. I have one in my A3000 and highly recommend it.
Keep an eye out on E-Bay for some Zorro RAM boards. They crop up from time to time and you can pick them up quite cheaply.
Definately upgrade the kickstart ROM. If you can, get a ROM switcher similar to what I had. That way you can install a 3.0 ROM to run OS3.9 and also use the original ROM (2.0 in an A1500, I think) for games that need it. There is also a handy utility called that can allow you to set up your hard drive to boot a different Workbench depending on which ROM is active. I used it on mine to load WB1.3 (salvaged from the dead A2000 or WB2.0.
Finally, hunt around for a scan doubler. A Zorro one is quite rare, but Software Hut are supoosed to be getting some external ones in stock soon.