Starting out in Corporate Strategy

Looking for some advice...

Background

Been working ~10 months at an insurance company in a FLDP (rotational program). I am not based in US but the size of the company ranks around 250 if it were in F500. Recently offered a position as a Strategy Analyst. It is a fairly new team (established around 2 years ago) with only a handful of people at the moment (previous experiences include consulting and corp. strat. roles in other companies). 

From my experience on the team, they interact often with the c-level and have good exposure across the business, on the other hand you tend to be a 'jack of all trades' rather than have any in depth knowledge of a specific area. Some of the people I have talked to have suggested the Strategy team is "too high level", concepts are often theoretical and it is often detached from the actual business e.g. from customer facing roles such as Claims/Underwriting.

Role is more in 'connecting the dots', revolves around strategy development/planning at a division level and business unit level as well as occasional adhoc projects like partnerships, investments/divestment, this is not a corporate development/M&A role. I did enjoy my time on the team due to the diversity of projects and the culture is good.

Questions 

Conscious that I want to build a solid foundation to start off my career with opportunities for progression down the road.

Given the small size of the team, are my options for progression limited vs joining a larger team, say finance or treasury? What are my options down the road?

Not many people seem to start off in corp. strategy (they tend to move into it later down the road), is it a wise move to start off in this type of role or am I pigeonholing myself within such a small (and new) team? 

If i want to transition to consulting down the path, what would that path look like and is it an easy move?

Any insight is greatly appreciated. Thanks in advance for your help!