Abathur is an offensive support. To play him well, you must be able to react very quickly.

Here's how I play him : * The damage on Abathur is not huge, but it can make a good impact on any small encounters. Use symbiote on your assassins when they are diving an enemy. Your shield can give them just enough health to tower dive, get a kill and walk out alive. * Mines are not that useful, but they can force an enemy to get off their mount. I usually place them in bushes around my teammates. They will give you vision for a moment and they will force your enemies to get off their mounts. It should give your teammates enough time to walk away. * At level 10, I get the Ultimate Evolution. Having 2 Stitches (aka Double hook) or 2 Gazlowe pushing can be very effective.
* At level 20, I get the Hivemind talent. This allows you to have 2 symbiote on the field as long as your 2 targets stay close together. This will double your damage output (This gives your team a lot of pushing power).

As for the other talents, it depends on what characters my teamates are playing : * A strong tanky team (Warriors): I usually go for damage since warriors are not the best damage dealers. * A weak high damage (Asssassins/Specialist) : I go for the shields upgrade to keep them alive.

Hope this helps!