You don't have to wait any time. It's a different visa.
However, do note that if the visitor visa asks you anything about the rejection, or even if you're asked at the border, you may need to declare that they rejected you in the past.
The best you can do is to make absolutely sure you've included every piece of documentation they ask, in a nice, ordered fashion. Make it easy for them to find the information in your application. If you're not sure if you should include something - INCLUDE it. This is from what we've seen on here, one of the most common reasons you get 'not satisfactory answers' - include all relevant information.
For example if they ask for proof of a job and you don't have one, don't just leave it out, include a letter about how you're say, starting one with x next month and include a copy of the offer. (I'm not sure if that's on the application, but was just an example). Too often we see people who have jsut left out a document because it put then in an unfavourable light - if you don't like how it makes you look, include an explaination.
For example, one friend's application my bank balance shows as an negative as it was a shared mortgage account, but could simply include other statements showing the mortgage and assets, and the separate savings account as proof of funds.
Stand down wise, there is no reason why you can't reapply - unless it states so in your rejection letter. If not, prepare all appropriate documents, and go for that visa.