IF this is $600-$650 total:
Mossberg or Savage .22 rifle ~$150
Heritage .22 revolver ~$110 during Black Friday
Mossberg Maverick 88 during Black Friday $200
Ruger 9E (or LC9s if you want smaller pistol) $300-325 or Taurus PT-1111 for $230.
If the handgun is want to be kept as small as possible, like micro/pocket sized, then the price goes down to $200 and it's going to be a .380 ACP. Not exactly powerful, but it's cheap. Also, if you want a larger/duty size pistol, then look at LEO trade in Glock's in .40 S&W. Yeah, you may not like the caliber, but the price will be low and you can buy a 9mm barrel for $110 later and be able to shoot two calibers.
The defensive/combat rifle is really tough here. You're either going to spend a LOT of that $600 on a rifle and have nothing left for a handgun or you're going to get something very cheap that's questionable and also be stuck with a cheap handgun to go with it that's also questionable. One option is to buy a pistol chambered long gun, like the Hi Point for $300-325 or Kel Tec Sub 2000 for around $425 and get a pistol in the same cartridge so you have ammo commonality. So, in that sense, you could get a .22 LR handgun for little and the .22 rifle for little and still have something like $300 for whatever else.
Bottom line: you're not going to get a good rifle that's for defending your life for a small amount of money.
If you're not expecting any engagements or conflicts that require you to shoot more than 50 yards, then you can use slugs in the shotgun or take careful aim with the pistol. If this is strictly homestead defense, the shotgun and a handgun is nigh unbeatable and has been for over 150 years.
If this is $600 for a long gun and handgun:
Glock 17
DPMS AR-15
I'll throw in the Heritage .22 revolver again because you can get those so cheap and they're so valuable for small game gathering.