Here is a quick test for the toilet....Pour a full 5 gallon bucket into the bowl and see how fast it drains out as you are pouring.
If it flushes fine by doing this then the holes under the rim are probably clogged and the water flow from the tank is real slow making the flush real slow.
If it flushes slow then the clog could be in the trap for the toilet. Taking the toilet off the closet flange and pouring the bucket of water into the flange directly will tell you. Then you may get to try the reverse search into the toilet trap !! I've found toothbrushes in there slowing things down....not pretty and definitely a reason to replace your toothbrush!
If the clog is in the pipe you get to use coalnewbie's snake suggestion and since the toilet is off the flange you have direct access!
If you end up replacing the toilet I highly recommend Toto toilets. I have put in about 2 dozen over the years and never had an issue or complaint about them not handling what people dish out and never had an issue with the tank guts. I have probably put in more ADA toilets than regular height and would suggest that if you have older folks in the house. Last I bought one from a real plumbing store (Northeastern Plumbing vs. big box) they ran about $275 for what I think they called the Drake model, but it has been a while so I might have the name wrong. It was their basic model, but I know from my experience being a weekend janitor that they work better than Crane, American Standard & Kohler basic models.
If you feel like splurging here is a model that may keep you in the throne room forever!! http://www.faucetdirect.com/toto-ms982c ... 4AodOkwAOg