Depending on how much of a project this project bike becomes, you may find you need more tool that you think. The essentials for sprucing up a bike and normal tasks include a full sets of metric spanners, metric sockets (regular and deep socket), couple sizes of rachets, phillips and flathead screwdrivers, a drift (soft steel or brass rod for knocking out bearings/bolts/etc), multimeter, feeler gauges, impact driver and some more that will come to me later.
Other tools that you may need for unnexpected tasks are things like a utility knife, hammer, caliper, angle grinder, magnetic pick-up tool, bench grinder/buffer, dremel, adjustable wrenchs, plier set, torque wrench, pick, wire brush, and a place to put them all (a peg board at the least).
I am pretty much a Craftsman fanboy at this point. Practically every tool I own is Craftsman including the huge tool chest I keep everything in. In fact, not 10 minutes ago I got back from Sears to get replacements for a pair of needle nose pliers where the tip broke off, a LED magnetic pickup tool where the light cuts out sometimes, and a small rachet that jumps out of rachet sometimes. No questions asked. Guy was like, "OK heres 3 brand new tools, have a nice day" Can't beat it.