Looking at your added note, if you intend to use a plane for thicknessing and flattening larger panels than can fit in your jointer or planer, then you will need a combination of planes.
First, you would possibly want a scrub plane that is used to remove a lot of material quickly. This would be needed only if trying to take a board down in thickness a significant amount as it can take shavings almost 1/8" thick, but does not leave a smooth surface behind. It is purely a roughing tool. Instead of a scrub, you could also use a #4 or #5 set for rough work, but this would not be the same plane you use for smoothing, or at least you would need 2 separate blades - one for scrubbing and one for smoothing.
Second, you would need something like the #6 or possibly a #7 or #8 for the flattening process. This will take out most of the roughness left by the scrub plane. On wood without much figure, this could actually leave a surface ready for finish if the plane is good and sharp and set for fine cuts.
Third, you would need a smoothing plane, commonly a #3, 4 or 4 1/2 size plane, to bring the wood to final smoothness. My first choice is the no. 3. I just like it's size weight and it fits my hand well. For larger panels like a table top, I use a 4 1/2 size plane because of the wider cutter. This plane, if tuned and set up correctly, will leave a surface ready for finish.
As you may guess, hand plane users soon become plane collectors because there are so many different variations of set up for various applications. For many of us, it is easier to have multiple planes, already setup for a task, rather than to have to change the settings of the plane each time we use it. For the purpose of thicknessing and flattening boards, there are actually several steps to follow in order for the process to go as quickly and efficiently as possible. You could do it with only one plane, but you could easily take all day for one board if trying to do it all with one plane. If you just want to buy a plane to start getting into them ane learning how to use them, go pick up a Stanley Bailey No. 4 or similar (should be able to find a decent user for less than $40), learn to sharpen, tune and use it and then decide if you want to spend the money for the LV or a Lie Nielsen. Even if you never actually use that old No. 4 much, what you learn from the process of cleaning, tuning, sharpening, etc will be valuable no matter what type of plane you decide on. As a final comment, the one plane that most folks, even power tool users, find to be indispensable to have handy is a good low-angle block plane. It has many uses and is the one that I use on almost every single project. In fact, I have several. My reason for this is to avoid sharpening. I go ahead and sharpen them all at once and then when starts to get dull (I don't wait until they are completly dull as that would make the sharpening process take much longer), set it aside. When all of them get dull, then I sharpen all of them at the same time. See what I mean, hand plane users usually become plane collectors in a fairly short period of time.
Doc