The only real way of doing it if you get married is to file an I-130 for him and sponsor him for permanent residency. He wouldn't qualify for any kind of non-immigrant status because he would be married to a US citizen who would be resident in the US, so he does not have non-immigrant intent.
If he has a girlfriend who is a US citizen, that can cause problems if the subject comes up because CBP may think he has non-immigrant intent.
It would certainly be a major advantage to be a permanent resident of the US, because he could apply for any job and not be subject to the many restrictions that categories like H-1B and TN-1 have.
On the flip side it's important to note that becoming an LPR brings certain responsibilities with it, for example he must forever more file a US tax return and his tax home must be the US, because under the tax treaty a claim of permanent residency in the US is exactly that.
You must also as a US citizen file a 1040 tax return every year and a Form 2555 if you are resident in another country. In order to be able to sponsor him for permanent residency, you must provide copies of your US tax returns for the last three years, so if you haven't been filing 1040s, you need to get that sorted out.
You need to get it sorted out anyway if you haven't been doing it for your own benefit. The IRS usually requires seven years of returns if you've never filed.
It's actually quite simple to do, basically you declare your foreign income on Form 2555 (or 2555-EZ) and that usually means you declare zero on the 1040. You only have a problem if your income has been above the foreign income exclusion limit for the last three years, as they put a cap on it in 2006. For 2008 the limit is $87,600. So if your income is over that in USD, you will have to pay some US tax for the last three years.
Once he becomes an LPR, it's generally a good idea to remain in the US until he gets citizenship. A lot of people get into difficulties because they move to the US (or vice versa, move to Canada) become LPRs and then decide they want to move back, but want the option of moving back again at some point in the future. Well, maintaining LPR status is a pig if you live outside the country, and you have to file
taxes as a resident of that country.
So if you're going to move to the US, make sure you're both okay with the idea of staying for several years at least.
Steve.