The "loan type" (FHA, VA or Conventional) pertains to how the loan is insured or guaranteed if the borrower defaults on the loan and the loan goes into Foreclosure.
If the loan goes into Foreclosure, then the property is sold and the proceeds go to the lender. If the lender loses $1000 (for example) because of the Foreclosure, then FHA (Federal Housing Authority) agrees to compensate the lender in the amount that they have lost ($1000 in this case) so that the lender is "made whole." The VA (Veterans Administration) works roughly the same way. Both FHA and VA have limits on the amounts they will reimburse. FHA loans and VA loans are considered "government loans." Because FHA and VA are "on the hook" if the borrower defaults, they have guidelines for underwriting the loan (i.e., they have specific ratios, etc. that the loan must meet). Therefore, these loans are usually tougher to get because they do not have as much flexibility in their guidelines as a "conventional" (non-government) loan has. FHA loans are now considered to be "safe" for investors (as opposed to sub-prime mortgages) because of their stricter guidelines.
A "conventional" loan is a loan that has "private mortgage insurance" (or "PMI" or "MI") which operates as described above in the case of foreclosure. If a borrower on a conventional loan defaults and the lender forecloses and loses $2000, then the private mortgage insurance company (not a government agency) cuts a check to the lender for $2000 to make the lender "whole." As stated previously, conventional loans generally have more flexible terms than government loans.
If the amount of your loan is 80% or less than the value of the property, then Mortgage Insurance will not be required at all (because a Loan-to-Value ratio (LTV) is not considered to be very risky to the lender). For example, if the property you want to buy is worth $100,000 and your loan amount is $75,000, then you have an LTV of 75%. If you default on the loan, then it is very unlikely that the value of the property will drop so far that the lender will lose money (which is why MI is not required for a loan with such a low LTV).
Regarding advantages to you (the borrower), I don't think there would be any advantages either way (other than that a conventional loan could probably be approved and closed more quickly than a government loan). Mortgage Insurance is there for the benefit of the lender; not for the benefit of the borrower. If you're trying to decide on a mortgage loan, I suggest going with the loan that gives you the best loan terms and the best interest rate.
Make sure you understand the following:
1. How long is the term of the loan (10 years, 15 years, 30 years, etc.)?
2. What is the Interest Rate?
3. Does the Interest Rate adjust or change at any time? (If yes, this is considered an Adjustable Rate Mortgage or ARM. If the IR does not change, it is a "Fixed Rate" loan.)
4. If the Interest Rate adjusts, when does it adjust (after the third year? second year?) and how much can the Interest Rate go up (or down)?
5. Are there any "Prepayment Penalties" on the loan? In other words, if you pay off the loan earlier than the original term (which almost everyone does), is there any penalty? (Sometimes there are prepayment penalties only in the first few years of the loan.) If these prepayment penalties exist, do they apply if you pay "additional principal" every month? (For example, if you add an extra $100 with each payment, will you be penalized?)