Unlimited doesn't mean oversold and limited disk space doesn't mean they don't over sold...anyways, most of the host use unlimited terms just for marketing (to get client)...they don't really provide you with unlimited space....each and every host including some famous one like hostgator blah blah etc has limited disk space for each user..only difference is that they don't exactly tell you how much space they are giving on one account...If you check their Terms & condition..You will find that they have cleared mentioned about limited space,bandwidth and cpu usage..if you exceed that limit..they will ask you to move your account on some higher coast plan or might just suspend you temp.
You should not jump for a host that offers 1 or 5 GB limited space...maybe they are selling 5 GB space on 500 GB or 1 TB hard disk...you can do maths how much domain they can host & over load server.
It also depends on data center & more on their Server.
Do search for a review if any...check the port speed..gud if they offer 100 mpbs, Bandwidth they are offering and most important write to them and check out how long they take to reply back...Buy a small package like for 1 month..some good host offer 1 month packs..so you can review..if you don't like their service..you can move on and won't have any fuss for money back from them.