No it will not AF on the D3000. MF is difficult especially if your subject is moving, and if you don't replace your focusing screen. The small viewfinder of the D3000 makes it especially hard to manually focus, and it's worse if you don't have a focusing screen designed for manual focusing.
You could still get a 35mm f1.8, it's twice the price of the 50/1.8, but that's one of your few options for primes when you are on a D3000. Others include the Sigma 30/50/85mm primes and the 24/50/85mm f1.4G lenses, though the Nikkors are very expensive.
When looking at sigma lenses, if the models have the HSM designation, it means it can AF on your d3000. For tamron, lenses with BIM or PZD designation will AF with d3000. For Tokina , you have to read up on the specs or ask people or try the lens to be sure. For Nikon, any lens with AF-S or AF-I will AF on the d3000.