Many methods have been developed for planning the motion of robotic arms for picking and placing, ranging from local optimization to global search techniques, which are effective for sparsely placed objects. Dense clutter, however, still adversely affects the success rate, computation times, and quality of solutions in many real-world setups. The current work integrates tools from existing methodologies and proposes a framework that achieves high success ratio in clutter with anytime performance. The idea is to first explore the lower dimensional end effector's task space efficiently by ignoring the arm, and build a discrete approximation of a navigation function, which guides the end effector towards the set of available grasps or object placements. This is performed online, without prior knowledge of the scene. Then, an informed sampling-based planner for the entire arm uses Jacobian-based steering to reach promising end effector poses given the task space guidance. While informed, the method is also comprehensive and allows the exploration of alternative paths over time if the task space guidance does not lead to a solution. This paper evaluates the proposed method against alternatives in picking or placing tasks among varying amounts of clutter for a variety of robotic manipulators with different end-effectors. The results suggest that the method reliably provides higher quality solution paths quicker, with a higher success rate relative to alternatives.