You want "better acceleration" and "more speed". First you need to find out what you have to see what it will take to upgrade the 350. The numbers on the engine block pad at the front of the passenger's side (under the alternator) may help to identify what you have and what you will need. During the 70s, the 350 was detuned and raped of horsepower for the sake of emissions. Some 350s had as little as 145 hp, less than that of a V-6 in today's cars. You may need to change heads, as well as cam and lifters, and pistons as well as intake, carburetor, and distributer to achieve your goals.
Better acceleration can be a combination of engine torque and gearing of the transmission and / or differential. Are you wanting tire smoking launches and fast 0 to 60 mph times. Do you cruise around town or mostly highway? Are you willing to accept 10 to 14 mpg?
You can get 400 hp or more out of your 350 if you want to spend the money, but the crate engine may be your most economical choice and comes with a warrantee.
BUTTTTTTT - then you still have the transmission and differential gears that are nice and adequate for the normal cruiser, but too weak and wrong for "better acceleration" and "more speed".
More info needed on what engine you have.