I've done both. Purees at 16 weeks with baby number 1, because everyone else was doing it (or so I thought) and I honestly didn't know anything behind the reasons to wait.
Second baby was exc. Breastfed and I didn't start weaning til 6.5 months. Mainly because we took a two week holiday when she was just approaching 6 months and it was easier to stick to breastmilk alone and wean when we got home than try to find baby-friendly food abroad.
Having done it both ways and having read the information Emmajaine and Sprout mentioned, I would leave it as late as possible.
I took the same opinion as Sprout, that if there is a risk that the baby's gut has not matured to handle solids, why risk it. I'd rather wait a few more weeks and lessen the risks.
I also did BLW with my second and skipped purees.
Oh and just to add, breastmilk and formula is actually higher in both fat and calories volume for volume, than most first foods, the exceptions being sweet potato (with no added water), avocado, and bananas.
So if you have a baby who is not gaining as much weight and is low on the percentiles or dropping percentiles, it makes more sense to feed more milk than to feed more solids or purees.
Oh and before 1 year, milk should still be the main part of a baby's diet, which is another reason why BLW is good, because it helps to keep milk as the main source of nutrition with foods 'complimenting' and boosting the diet, rather than food replacing milk (and incidentally, studies have found that babies weaned before 6 months tend to take less milk, so food often does replace milk when it really ought be be additional to the milk.)