The size sounds fine. But what will happen should the well fill during a heavy rain? If your channeling all that water into the area that you have, you could fill it up pretty quickly. Even though there's sand at the 4' level, what's below that? (No need to reply; just consider this.) At my home, I dug a well pretty much like yours but when it fills, I have a french drain take the excess to the street. You see, my thinking is to put the water in the ground first, then have the excess go into the sewer. I used 3/4" gravel. Not p-gravel; not modified bedding gravel. The smaller the stone, the less available 'air-space' there is for water to occupy. In other words, the smaller the gravel, the more volume is taken up by stone and there's little left for water! Use 3/4" gravel. Yes, line the well first. I used filter fabric. Not landscape fabric. You should be able to get it at the gravel yard / quarry. If not, ask them or any excavator in the Yellow Pages where it can be had.
Line the pit with the fabric first, overlapping it by 3-4". Leave enough extra to wrap over the top once the well is filled with stone. Leave enough room on top for 4" of dirt. After you completely wrap the gravel in the fabric, put dirt on top of the fabric/well for grass. (This, of course, if you intend to make the well invisible.) Continuing ... I don't run my downspouts directly into the well. I 'layered' the top of my well such that it's lowest point is in the middle and the edges are about 1-2" above that. Kinda concave in shape; like a shallow bowl. And in the middle, I have a vent that sticks up about 1" above the dirt line such that when the water starts to fill the concave area, it rises above the vent and drains into it. (Nothing drains out of my 'bowl'.) By running your pipes directly into the well, you will "pollute" it with the junk that's coming off the roof. (Asphault granuels, leaves, and all kinds of debris.) My verticle vent-pipe is only 6" long. The shorter it is, the more water you'll get in the well. So keep it short. My french drain to the street is about 8" from the surface. This way, the well can continue to fill while the excess water is still being carried to the street. (The french drain 'level' needs to be below that of the bottom of the vent-pipe.) The french drain is perforated, flexible, black pipe that's layed on top of 2" of gravel and totally wrapped in filter fabric. The slope is about 1/2" per foot, minimum.
I know this sounds like a lot but if you sat down with a pencil and paper and drew it out, you'll see much better what I'm trying to say. If anything is unclear, e-mail me directly. My best to ya and hope this helps.
PS: If you intend to fill the well to the top of the ground with gravel, you still need to protect the top with some sort of 'filter' to keep debris out. Filter fabric isn't exactly what you'd like to see once you wrap the well up. One suggestion is to wrap the well to about 1-2" from the top with the fabric, then use landscape fabric for the rest of the way. It comes in all kinds of colors and sizes. When the top layer starts looking yuchy, you remove it down to the filter fabric, clean it off, then fill it back up with landscape fabric again.