How do I do collision detection between the player and an obstacle / pickup?

There are many techniques for collision detection.  In this module, my advice is to keep it simple. The simplest form of collision detection: 
glm::length()

If the distance between two objects is below a threshold T, register a collision.
if (glm::length(p-q) < T) 
   // collision



This requires that you know p and q.  If you have a large number of obstacles / pickups, store them in an std::vector.  Then, when performing collision detection apply the above algorithm for each object q with the player p.

A natural place in the template code to do collision detection is Game::Update().

High