Burgess is there in Dressrosa for one sole reason only, to gather DFs. His initial focus was on the elusive Mera Mera no Mi but bad luck it fell into the quite-capable hands of Sabo.
Losing the Mera Mera does not mean exit for him as Dressrosa turned out to be hosting an abundant of devil fruits and it is up to him to pick and choose. Of all the DF abilities present, I fail to see a REALLY good reason to aim for the Gomu Gomu, other than the fact that Luffy was weak at that instance and the opportunity was there to "collect" it, not specifically aiming at it though.
Also, Doflamingo is getting weaker from his fight and perhaps there will be chance to grab this one as well?
But apart from these three (Mera, Gomu, Ito) there are others e.g. the Gravity of Issho's, Ishi Ishi (Pica), Beta Beta (Trebol), Hira Hira (Diamante), Buki Buki (Baby 5), Giro Giro (Violet), Hobi Hobi (Sugar), etc.
In my opinion, Burgess being a melee, wrestling style fighter, the Hobi Hobi will suit him nicely as it compliments his fighting skills.
1) In the midst of chaos, what should have been his top priority DFs from Dressrosa?
2) Which of the DFs abilities that he should claim for himself?