– helium balloons typically reach 32km (20 miles), a $300 (£200) budget is enough (provided flight authorisation is granted), and this takes about 3 hours (e.g. see this video at 7:38)
– edge of space is defined as 100km (Kármán line, 99.99997% of the atmosphere is below that)
– the forthcoming SpaceShipTwo flights are carried to 16km by a launcher, then reach 110km in about an hour
– the International Space Station orbits at around 350-400km
– the Appolo program modules that got to the moon were launched by Saturn V rockets : they went up to 67km with the first stage in about 3 minutes, then the second stage got things up to 185km in about 6 minutes, and the third stage did the orbit insertion just a few kilometers higher (2.5 minutes) and finally the trans-lunar injection (6 minutes burn). See this page for a nice simulation of a full launch, including plots and precise numbers.
So, on a low budget the main aim is to bridge the gap from 32km where the balloon stops to 190km where trans-lunar injection can take place…