smoothing

Here is my problem. I jointed a hunk of plywood (birch) to a 6 inch wide maple board. This is the top to a window seat I am making. The long and short of it is the good side ended up being the side that is about 16th high, I sanded and now I have a rounded effect that I know I will be able to see later on, when I paint it. So I am thinking I need to plane the surface, with a hand plane. Problem is, I don't own one and for the most part have never used one if you exclude high school some 20+ years ago.
Other detail, plywood is 13x72 and the maple is 6x72 all 3/4 (except the problem point. Biscut joint if it matters.
What sort of plane do I need or other options?
Jack plane, smoothing plane, wood plane, damned if I know what plane. Should I get one of those knight planes, it sounds as if they are so good a fool could run one and get good results. (I would practice first as I would consider myself more then a fool with a plane in my hands!)
thanks
ow would like a general purpose plane but my imeadiate need is a smoothing plane, I think. I have never used on before but so I really don't know what I am looking for. I looked at Lee Valley's web site and it looks like there are a bunch of choices.
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It takes a while to become proficient using planes and I think that you will have better success if you practice before trying to fix a meaningful project. For a first bench plane I would get either a #4 or #5. I would also read about plane tune-ups. With the exception of the best planes they all need to be tuned before using. I do not own a Knight or Veritas but have read great things about both. I own a bunch of old Stanley's and new Lie-Nielsen's. The Stanley's needed lots of work before using but the Lie-Nielsen planes were perfect out of the box.
I hope that this helps a bit. - Bob McBreen
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Mike Coonrod wrote:

Use any plane that you have.
I've never had to curse my Lie-Nielsen planes, but my two Stanleys are another story. After *much* tuning they cut just as good - well, almost as good - as the Lie-Nielsen planes. The difference was five minutes to final-hone the Lie-Nielsen planes vs several *hours* of tuning the Stanley planes. Of course the Stanley planes each cost less than $50 each at the local Lowes while the Lie-Nielsens were $225 and $300 respectively. I use the Stanleys first to make the rough cuts and finish things off with the Lie-Nielsens, just as I use a cheap blade on my Unisaw to rough cut lumber and a more expensive blade for final cuts.
I had the Stanley planes for several years, mostly sitting on a shelf. Everytime I tried to use the block plane or the #4, I gave up, totally frustrated. Finally, after much discussion with the people at the local Woodcraft store, I bought a Lie-Nielsen, set it for a fine cut and became addicted. Right out of the box, that plane outperformed anything that I had ever used before. After spending five minutes total to hone the blade and reassemble the plane, it cut perfectly. I went back to the Woodcraft store, bought four Japanese water stones, a leather strop and their yellowstone dressing for the strop, a video to show me how to tune a plane and spent the better part of a day tuning up the two Stanley planes. By the time I was through, I understood how a plane works, how to do basic tune-ups, and most importantly, how to use a plane as it was meant to be used.
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