My kids have always had access to computers. Here are a few pointers as you consider what to get:
Macs have parental controls built into all of their computers. You can decide how many hours a day your child can use it, what programs can be accessed, what is the earliest it can be turned on in the morning and what time it automatically shuts off at night. You can filter contacts - if any, websites, etc. For a toddler, this will be imperative if you plan to allow your child to use the computer without you sitting right there.
IPod Touches are a good size for little fingers and not horribly expensive if it's dropped, cracking the screen. iPads are a better viewing size but are a bit wieldy for a toddler to hold or carry. If you go this route, invest in a heavy-duty case that will absorb the shock of being dropped. One other thing to consider is that less software is currently available for an iPad than a computer, but the tactile interface is user-friendly.
iPads & Touches have some parental controls in the form of restricting the browser and a few main apps as well as whther multi-player games can be accessed, but it is not by specific users on the device, it applies to the entire device. To my knowledge Kindle Fire has no parental controls although a recent software update does allow you to add a password to access the device.
My kids have had access to computers since they were born, and other than making sure parental controls protected them from inappropriate content and setting up opening and closing hours so the youngest didn't stay up all night, we've found they've moderated themselves time-wise because it wasn't forbidden fruit.
