If you go for a M3 make sure you check the viewfinder/rangefinder very carefully. Shine a light through the front and look at it from the back at an angle. You are trying to see if the prism is oxidizing. Youxin Ye pointed this out to me on the first M3 I brought over to him for a CLA. It took me 3 tries to get a M3 that didn't have this problem. There are a couple of people that can resilver the prism but it is expensive or a in depth
DIY repair.
As far as M3 vs M4 the standard answer is M3 for 50mm and up or the M4 if you want to shoot a 35mm and have framelines. M3 finder is almost life size image so shooting with both eyes open is pretty easy.
*BUT* if you are looking to shoot kids/fast and want Leica I'm going to recommend the M5 or a CL or CLE. The meter and display in a M5/CL means you can follow kids quickly through changing lighting and adjust without moving the camera from your eye. The CLE has aperture priority auto exposure so it is even faster for this kind of situation.
Edit: Or one of the larger fixed lens RFs and it would leave a huge amount of money left over for film. If you want the precise feeling of the Leica something like a Konica IIIa is beautiful and a true 1:1 viewfinder that adjusts for parallax
and frame size.