I have had great success using Rust-Oleum brand Filler + Sandable Primer, which you can find at Lowes and also auto part supply stores. This primer has a high-build that is designed to help fill in imperfections AND is also very sandable which aids in the refining process. On top of all that, it dries pretty fast, so you can actually start doing some sanding within an hour or two pending how thick you have put it on.
Depending on how deep your wood grain is, I would suggest layering your primer on in even coats, waiting some time for it to dry up between coats. If in the end, you are still getting some wood grain, you can always use bondo to fill it in.