From what I understand, reducing the size does indeed vastly improve the FPS, especially for slower PCs where the FPS increases by untold amounts just by going for a 2x2 or even 1x1 embark(with DFhack). Some people also use the 1x1 as a challenge, to see how much skill they have at DF. Because the smaller the embark, the harder the game is. I guess most people dig a hole in the ground then and use a multiple Z-levels for areas where 4x4 embarks would use one.
But other than that, it is playable. Harder, but possible. I guess that you can make the path for invaders longer by channelling yourself an entrance on the surface and make a long hallway, which you can then fill up with traps as you would normally. After the hallway you can simply dig the main stairwell and go down. This also allows for a lot longer time for your dwarves to get in.
That you won't have to look for something can always be accomplished after you get a bookkeeper and accurate stockpile records. (You won't actually have to get "highest precision" right away, if you don't have any more of an item or category than the accuracy gets you, such as you don't have any more of an items than those 400 stones, then you can actually just get "medium precision" and you will be fine. When you see inaccurate numbers with a ? behind them then it's time to get one level higher precision.) You can then go into the status menu with Z and select Stocks, and you can find any item by pressing tab and then going into its category, finding that item, and pressing Z.
Also, a 4x4 embark is default