Some flashes do offer "high speed sync" but usually they eat up a lot of power reduce their usable distance from flash to subject. There are some other triggers such as the radio poppers that allow faster sync speeds, but that is a whole other subject.
Usually with a cheap flash you trade off one ore more of the following: TTL metering, Power, recycle time, power adjustment, and/or build quality, etc.
There are some very good third party flash units, you just need to identify and understand their abilities and limitations.
For example, putting together a stobbist kit, you don't care about TTL metering, but you do want as much power as possible especially using umprellas and other modifiers and you want a flash that easily lets you adjust the powwer setting. Fast recycle is nice but usually you can afford a moment between shots because you will likely be repositioning your model or subject anyway. Something along the lines of a Vivitar 285 fit this description well.
Now I you are shooting a wedding, you need Lots of power especially to bounce in big halls, fast recycle time, and TTL metering is quite useful in a fast paced environment where there are no second chances to get the shot. You really need a a Canon 580ex II, or top of the line Nikon.
Really most flashes in the sub $60 range are junk, around $100 there are some pretty decent units, some limitations, but very useful for many things. getting up in the $250+ range are where all the really good units fall.
Just for general picture taking and hobbyist use the $100-250 range is a good balance of price and features IMO.