A couple good questions here. First, you can buy a home if you owe money to the state. The issue would be with getting a mortgage (you could use cash, or contract for deed if you're really desperate!). So the answers below seem to relate to your ability to obtain a mortgage, and they are sound answers - it all depends on the nature of the debt you owe the state and if the is a payment plan in place.
For the community land trust you will need a mortgage. For information about land trust pros and cons, you can contact the Rondo Community Land Trust in St. Paul at 651-221-9884, and Community NHS, also in St. Paul, at 651-292-8710. Community NHS is also a great resource for first time home buyers and for credit issues. Best of all, most of their services are free!