Pay now or later...
The $400.00 ceiling makes it difficult to make a strong recommendation but here we go:
For immediate purchase
The strictly 'hunting/target' handgun in your price range I would recommend is the Ruger Super Blackhawk in .44 magnum. Based on the friends I have that have actually been boar hunting the .44 magnum is the lightest that should be carried in the field. The ammunition is more expensive than others but the capability is worth it in the field.
My best recommendation
Find yourself a Smith & Wesson K-22. It will have at least a 6 inch barrel and will hold 6 rounds of .22LR. They can be found for around $400.00 used. Then each time you buy a 50rd box of .22 take the difference of what it would have cost to buy a box of .44 magnum ammunition and put it into a separate savings account.
In relatively short order you will have acomplished several things. First, established if you actually enjoy shooting handguns. Second, increased you ability to put the round where it needs to be which translates into more ethical hunting. Third, saved the money needed to get the .44 magnum to hunt the game in question.
Other possibilities include the potential to use the K-22 for squirrel hunting depending on jurisdiction. The K-22 could also be used for bullseye oriented shooting although will not be as competitive as a semi-auto handgun. Also, if after shooting the K-22 awhile you determine that you are just not into handguns then you can very likely sell it for roughly close to what you paid for it if you are a conscious shopper.
I honestly believe you will enjoy handgunning more by starting with the rimfire and working yourself into a 'hunting' handgun.
FWIW and respectfully submitted.
