Advice on Toro T-bar

So my dad gave me a 36"tbar. And I have to buy a new trans for it because it's stuck in 3rd and I need it to be quicker for my sulky. But anyway sometimes it fires on the first pull and sometimes I have to pull for 10 minutes straight. Y'all think if I just bought a new carb and put it on it would start more reliably. I noticed if I kill it with the throttle instead of the fuel shut off it's harder to start up again. So if y'all had some advice that would be great. Thanks in advanced!