The issue with the unmodified A1000 (ones you have to use a Kickstart disk to boot) is that they only have 256k in the RAM tower used to load Kickstart. With 2.0 Commodore went to 512k Kickstarts which are obviously too large to fit in that RAM. This RAM is totally separate from system RAM so it can't be upgraded.
You have a few choices.
1) You can get an Amiga 500 which can use the 512k Kickstart ROM chips. This is the easiest choice and should be relatively inexpensive nowadays.
2) Try to find a Kwikstart (I think that was what it was called) board for the A1000. It was made by the same company that made the Multistart boards for the 500/2000, DKB, and allows the 1000 to use the same Kickstart ROMS as the 500/1000. This is probably on par with the difficulty of finding a Phoenix replacement motherboard for the 1000 for sale. These things are extremely rare to find outside a 1000 if you ever find them or sale.
3) If you have extra System RAM you can get a Kickstart image for 2.0 or 3.1 and use ykick or Twinkick from Aminet. These programs load the kickstart image into system RAM and then reboot the Amiga 1000 using that image instead of the 1.x image in the Kickstart RAM tower. You will lose about 512k of system RAM though and your computer will take longer to boot since you'll have to load your original kickstart, then boot with a disk with the program and kickstart ROM image which will then reboot the machine to use the new ROM.
4) If your really adventurous you can try this document from aminet: KickWOM.lha (in Docs/Misc)which is supposedly to modify an A1000 to load 512k Kickstart images.
Good luck.
