I have a pretty good idea of what my first set from each wave was, but I don't usually have a precise order of each wave past that.
2001: was Kopaka, Followed by Lewa, Gali and Tahu (I'm pretty sure in that order). I didn't get Pohatu until a couple of years later. I always consider Pohatu as my last 2001 set as in My opinion I technically never "got" Onua, but rather found the parts to build him in various random part hauls, but that's probably just me being difficult.
2002: is the only year I don't have any real idea of. I know I got all the Bohrok, Bohrok Va, and Toa Nuva as well as the Boxor and the Bahrag, but all I know for sure of the order is that the Bahrag were last (about 4 years ago when my grandparents happened across them).
2003: Kohrak Kal (and no other Kal), followed by Kurahk, followed by the other Rahkshi besides Vorahk. Aslo got Takanuva somewhere during that time, but I'm not sure when.
2004: In order; Keerakh, Vakama, Onewa, Whenua, Lhikan, Ahkmou, Matau. This is one of only two years I'm absolutely certain of the exact order I got them. Keerakh my mom grabbed for me on a whim, and the others through Ahkmou were birthday/Chrismas gifts. Matau I happened across at a flea-market a few year ago and grabbed.
2005: I didn't much care for the sets in 2005, so the only normal ones I ended up with were Vakama and Oohnorak. Somehow though I ended up with all 6 Rahaga. I happened across Roodaka (unopened!) a couple of years later at a thrift store and grabbed her as well.
2006: Nuparu, followed by Hewkii, Kongu, and Matoro all at once, then Axonn then Kazi, then Zaktan from a parts haul last year. This is the other year besides 2004 I know the exact order, mostly as a result of the unusual way I got the Toa sets. Basically, when I first sat the Inika, I though Nuparu was the coolest thing I'd ever seen, and I made sure everyone I knew was aware I though so. These people were the same people who would be buying me birthday gifts later that year and, as a result I ended up with 4 Nuparus. Three of these were promptly exchanged for the three other Inika mentioned. As for the others, I remebered Kazi was the last set I got that year which leaves Axonn as the second-to-last by process of elimination, and Zaktan I got recently enough to remember when it happened.
2007: I'm not as sure as with 04 and 06, but I'm pretty sure the order is something like Ehlek, Nuparu, Jaller, Knogu, Pridak, Hydraxon, Gadunka, Lesovikk, with Lesokivv being the only one I'm sure of as I got him just a few months ago.
Form 2008 onward, I really have no idea. I couldn't even begin to guess what order I got the 4 Phantoka (2 normal-size sets and 2 matoran) and 6 Mistaka (1 normal set, and 5 large) I have in. For 2009, I'm pretty sure Skrall was my first Glatorian (out of 5, 3 normal, 1 small and 1 large) and Mata Nui was my firs Glatorian Legend (out of 5, all normal size), but I'm not anywhere close to 100% sure, and in 2010 Tahu was the only Stars set I ever got, so I suppose he counts as both first and last(?) for that line.
I'm sure there are several sets I've gotten I'm forgetting, and I've bought a large amount of "assorted parts" online, so I probably also have the parts to build several sets I don't even know I "Have", but this is the order to the best of my memory.