Some suggestions

Welcome to the forum. It's always cool when someone gets the old car bug, so since you are new to American V-8s, here are some suggestions. First, decide what you want to do with the car. Are you going to make just a cool cruiser that will occasionally lite-em-up, or do you want to get a little more serious? Secondly, you need to set your budget. As the saying goes: Speed costs, how fast do you want to go? Having said that, if you are on a tighter budget, you should probably find out where the nearest car shows and swap meets are. These are great places to pick up a bargain on some speed parts. Your best bet would be to start with an Edelbrock low-rise intake with a 600 cfm carb. These can be picked up at reasonable prices. With the heads, find yourself a reputable machine shop and have them port and polish the heads. Also, you might want to consider a 3-angle valve job. One thing you should definitely do is have the valve seats hardened, because these cars were used to leaded gas, which is no longer available. This will keep your valves from being hammered into the valve seats.
On my own 62 Bird, I'm getting a little more serious. I'm converting the stock 390 FE engine into a 410 Mercury. By swapping in a 428 crank and a set of low-compression pistons, the engine is transformed into a raging torque-monster. Larger valves and better flowing heads, topped off with a dual-four barrel Offenhauser medium-rise intake and two 550 Edelbrock carbs. A set of headers will vent the fumes thru a set of glass-packs. All together, I'm thinking the engine should be good for about 450 horsepower.
What I'd really like to do with the engine is get an old Hillborn-style intake ( which was typically used in drag racing ) and have it converted to EFI. Of course my budget won't allow me to hit this plateau yet, but I can still dream.
Anyways, good luck with your Bird, and post some pictures if you get the chance. And if you need any more advice, this is the place to seek it.