We have both but no, I don't think they are both necessary. If you only get one, get the RnP. It is worth its weight in gold. DD1 had severe reflux and slept in it for a long, long time. For DD2, we used it as a bassinette downstairs when she was itty bitty, and now she sleeps it in ocasionally if she isn't feeling well/teething/ear infection (the angle helps things drain, plus I think she feels cozier and comforted because she is sort of nestled in there. We have the very first version of the RnP, and it hands down has been the best $50 we spent on baby gear.
I agree that you should try to borrow a swing before you buy one. Some kids love them and some hate them, and some kids just don't care. DD1 was meh on the swing. DD2 liked the one we borrowed so we bought one, but we rarely use it now.
Instead of the Bumbo, I reccomend this:
http://www.toysrus.com/product/index...entPage=search
I semi-agree with MsKitty about skipping the high chair, but I don't recommend going right to a booster. Baby has to be able to sit pretty independently to use that (or maybe just because my kids are small and there is extra room on the sides, they slide a bit). I really like the FP Space Saver high chair because it can be used before baby can sit unassisted (it reclines, has a higher back, and is padded). The BBB exclusive version has non-fabric straps that are a cinch to clean (and as an added bonus, DD2 uses them as teethers).
Mom to a spirited, red-headed, former 28-weeker 10/2009 and a more mellow monkey 12/2013.