I'm a Sports Handicapper - I sell sports betting picks, and have been doing so with a company for a long time with other handicappers. Now, i want to break away and create my own service and my own website. I want a website that allows users to first be able to create a free account. Then, i want them to have the option to sign up for "1 Day of Service", "7 days of service", "30 Days of Service", "60 Days of Service", "100 days of service", or finally "365 days of service". For each day that have signed up for (and paid for), I want them to be able to view all of the picks i put out for that day. So, my site would need different types of user accounts and each account would only be able to view my picks for a limited amount of time (the amount of time they sign up for).

Is there any software packages that I can buy (for some one who has fair experience, but not a lot) that would allow me to do this? Or am I gonna have hire someone & fork out a bunch of money? thanks!

You can certainly use something like Joomla, but it will take you much longer to understand how to use it than to write your own code from scratch!
You need a full e-commerce solution, correctly ADAPTED to your needs: only a coder can do that, not ANY IDEs or so-called "customisable software package"...
Why don't you post your request to rentacoder.com? You may be surprised by the "costs" of some bids...

Try Joomla. This is a software package and it gives you all the tools ready-made and you can customize it. Http://joomla.org
Good luck!