Are you starting out on an unmanaged VPS, or otherwise some dedicated server of some description?
Otherwise you won't have a direct choice in control panel software - just in hosting provider, who in turn will offer one or more control panels for you to utilise.
In terms of linux hosting, there are probably 3 main control panels that are popular (in alphabetical order!):
Which is "best" is a point of hot contention - I would say that each one of the above has its advantages over one or more of the others. Overall, I find Plesk to be a very stable and capable control panel, but others will shout very loud for their own preference... you just have to take a look and decide what you like etc.
I suppose for the sake of "completeness" I should also mention
Ensim, although it isn't really in the same league IMO.
All of the above are not free though. If you want a free control panel, your best bet is probably
Webmin / Usermin.
In terms of starting out with a hosting business, I believe that you're best taking either a multi-domain shared hosting plan (check with the provider as to whether you're allowed to resell on that - it will vary), a reseller plan, or a VPS. Anything bigger than that is likely to be too expensive to operate with a small number of clients, and therefore doesn't make sense.
Of course, the other issue is whether you'll be able to provide an appropriate level of monitoring / technical proficiency for your service if you were to use your own hardware, or otherwise manage your own server - if you're just doing this on your own then I would suggest that it wouldn't be feasible for you to be able to respond to (for example) a server outage in the middle of the night... how long would it be before you knew about it, and how quickly would you be working to resolve the problem?
If you take a managed VPS, or anything smaller (e.g. shared / reseller), this is the provider's issue to deal with - you can therefore focus more attention on your customers, and of course getting more!
