You can look up the relevant statutes here:
http://ct.gov/dps/cwp/view.asp?a=2158&Q=294508&dpsNav=|#firearms
and search the text here:
http://search.cga.state.ct.us/dtsearch_pub_statutes.html
But basically it tells you what you can't do rather than what you can.
As 209 said you can have in your house anything that isn't banned.
But be careful about storage if there are minors around.
This will tell you what items are banned:
Sec. 53-202a. Assault weapons: Definition.
Look it up in the statute search (see above).
Machine guns are legal but they must be full-auto only. If they are select fire then they are assault weapons and are banned.
If you are planning to be in CT for a while then get a handgun permit. It is probably the easiest CCW permit in the country and also avoids the waiting period for long guns.
Here is the FAQ:
http://ct.gov/dps/cwp/view.asp?a=2158&Q=294484&dpsNav=|
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