Make sure you allow the bar top to "float" on one edge. As temp changes, the top will expand/contract. If the entire thing is screwed down, you may get bowing/split in the top itself. An easy way to do this is to screw one side down from under your back rail, on the front rail (before screwing it down), make small slots about a .5" long. When you attach the front (or the piece where you would be standing behind the bar, however you orientate it), use a screw with a washer, and screw it in the middle of the slot. This will allow for the wood to expand/contract and not mess with the top itself.
Personally, I would do the top all in oak. I know it isn't cheap where you are, but that poplar is "paint grade" hardwood. It changes color quickly in sunlight, to something that will not look good with that oak. Better to go without for a week/month while getting the top done right, than get instant gratification and want to redo it later. YMMV.
Another alternative would be to get some of the oak plywood, and then get some of the thinner pieces of oak at HD and use it as banding around the plywood edge. This gives you a stable top that will not move on you due to temp/moisture content, looks nice, and probably come in a bit cheaper as well. Just a thought.
