New to guns and first time owner.

Ammo are expensive!
I bought 500 rounds at Dick's when they had sale past weekend.
$11.99 for box of 50 Winchester 9mm. Should have bought more. They sure do go fast. Lol

1, What is good hollow point for M&P 9mm full size for home defense?

2, Is there cheap places online for 9mm ammo?

You'll have to experiment with hollow points. Each pistol has it's own likes and dislikes. I went through several types before I found brands that would work in all my pistols (I don't like to have to have different types for guns in the same caliber). Remington Golden Saber, Federal HST work.

Cheap on-line ammo? Not as cheap as you hope, but better prices exist (unless you have a good Wal Mart nearby). I have been ordering lately from SGAmmo.com. Their stock varies literally hour by hour, but they have been reliable for all orders I've placed.

Before asking "What ammo should I use?" you should ask "What should ammo do, what shouldn't it do, and how is it tested?" I recommend the following:
Handgun Wounding Factors and Effectiveness from the Firearms Training Unit of the FBI
Basic Wound Ballistic Terminal Performance Facts by Dr. Roberts (DocGKR)
Ordnance gelatin test assessment for rifle and pistol calibers by Dr. Roberts (DocGKR)
What's Wrong With The Wound Ballistics Literature And Why by Dr. Fackler

For specific recommendations I start here:
Service Caliber Handgun Duty and Self-Defense Ammo by Dr. Roberts (DocGKR)
Then here:
9mm Ammo Quest on Youtube by ShootingTheBull410

There are countless threads on this topic. I'm using Hornady "Critical Defense." It feeds 100% in all my 9mms as well as an M&P .45 ACP. Other forum members have different preferences. My opinion is that there probably isn't much difference in effectiveness of modern, currently produced hollow point ammo.

No ammo is a death ray. It's up to the shooter to score effective hits.

I use Speer Gold Dots 124gr +p. There are a few other good manufacturers. Winchester Rangers, HST.

Look for Law Enforcement marked boxes. They are 50 rounds for $25 vs civilian boxes which are 20 rounds for $25

You can check Freedom Munitions and SG Ammo for some good prices.

I like Freedom for the range stuff and use their 124 gr RN for that and then use the 124 gr Speer Gold Dot for carry, which SG Ammo has at a good price most of the time.

I also like Gold Dots and HST.

Some good online sellers are:

Sgammo.com

venturamunitions.com

ammunitiondepot.com

__________________
USAF, 69-92
Vietnam, 72-73

I love the 124gr HST... I buy mine on SGAmmo and get 50 for about the same price as 20 local...

There are some really good performing hollow points these days. Speer Gold Dot, Federal HST, Ranger PDX-1, Golden Saber, and the Hornady XTP. Pick one of those and your really can't go wrong as long as it functions well in your personal weapon. You should be able to tell if your gun likes them after 4 or 5 magazines through it. No malfunctions, good to go. And do test it!

I prefer the Federal HST because it performs well from short barrel pistols like my Shield and XDm 3.8" Compact.

Cheap places on line for HD ammo? I find the best prices at SGammo, Ammunition Depot, Selway Ammo, and Target Sports USA.

Great experiance with:
Sgammo.com
Ammunitiondeopt.com

SGAMMO all the way