While I cannot offer the direct answer to the former part of OP's question, the answer to the latter part might shed some light also on the former, I hope.
As I wrote before in How were the members of the Varangian Guard recruited?, almost all the aspirant Varangians must have traveled to Constantinople to register on their own initiative (there was almost no record of dispatched the official recruiter in Western Europe).
In other words, the origin of the Varangian guards may reflect the demographic composition of foreigners those who stay in Constantinople and don't mind to make use of their weapons to offer service to the Emperor, at least to some extent.
It should be also noted that, as I also explained before in the linked post above, it is true that this service in the guard was highly rewarded, but they were also required to pay not so small amount of the 'registration fee' in the beginning. So, the foreign travelers who didn't have enough money also should have been ruler out from the entrance. The motive to join the Varangian guards for the Norsemen might also not been ascribed solely to the pure economic incentive.
(Added): On the other hand, the Greeks seemed to have regarded the Norsemen as loyal military retinue to their lord due to their people's traditional traits, as Anna Comnena express it by the mouth of John Ducas (The Alexiad, II-9):
'He [John Ducas] advised Alexius not to attack the Varangians......and as for the Varangians, who bear on their shoulders the heavy iron sword, they regard loyalty in the emperors and the protection of their persons as a family tradition, a kind of sacred trust and inheritance handed down from generation to generation: this allegiance they preserve inviolate and will never brook the slightest hint of betrayal' (Sewter trans. 1969: 95f.).
So, it also might been the Greeks that preferred the Norsemen as promising members of their guards to other Europeans, though the Anglo-Saxons were also known to join the Varangians after the Norman Conquest.
Reference: