I would say try that, and see what you can come up with. This will also give you an idea and turn the wheels so you can start looking at a budget place aswell. However, I suggest when shopping for reliable hosting not to base your choice soley on pricing levels. This type of shopping can cause you to be right back here on WHT in the near future (generally) requesting recommendations for another hosting provider.
How much web space? Unmetered bandwidth is pretty much on the same line as unlimited bandwidth, both of which are non-existant.
Price range per month? What exactly do you plan on using your web site for?
Heh, your best bet for something like that is an unmetered VPS server from FDCServers
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Continuously telling us that as cheap as possible is your budget is of no help, because that doesn't tell us anything. We need figures, numbers, digits, so we can better help you in your quest to find a crappy web host.
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You want Value for the money.
There are tons (well, maybe a couple of handfuls) of hosts that are charging what the market will bear, but also go the extra mile by providing little unadvertised niceties; like being pleasant, calm, knowledgable, so forth.
Believe me, go that route and you will come back here and kiss somebody's toe fuzz.
Go the dirt cheap, fall in the ditch drunk, sloppy host that cant figure out why his servers won't run and you will hate us all.