When you play Snake, you need to keep SAFE and try the best you can to NOT GETTING HIT (Isai's awesome phrase). If you are in a position when you will probably trade hits, then DON'T DO IT. It's not worth it, since Snake lives twice as long as you do. If you pressure him, you must know how to do it, and you must avoid any risks.
How useful are turnips on him?
Turnips are pretty useful. You can throw turnips and stay safe from his grenades by floating. You need to keep in mind that you can throw turnips while being at a 45° angle from Snake, while Snake can only throw nades at you when he is at a 90° or 0°/180° angle (I can even outcamp Toon Links this way). But you need to understand perfectly how Snake's grenades work, the exact time they blow up, the range/hitbox of the explosion, how the terrain can affect the grenade's trajectory (for instance, if he downthrows the grenade on Halberd's curved floor, the grenade will go at a 45° angled trajectory). You can also punish Snake's airdodge with a turnip (possibly glide tossed) if you have one in hand.
How effective is pressuring him?
Pressuring Snake is really effective, and it's the thing I mostly do when I play them. But you must know how to do it. If you just go aggressive against him without thinking, he will wreck you (especially if he is a good defensive Snake).
You can apply a lot of pressure when he is on the air (that is Snake's main weakness of course, and you as a Peach player must exploit it the best you can). Snake's usual options when falling are:
-Nair (if he is high enough for the Nair to end before landing) [You can punish this by breaking his Nair with Utilt, a turnip, a well spaced aerial, or by shielding and punishing]
-Airdodge [Use your usual airdodge punisher moves]
-Bair/Uair close to the ground [Shield and punish]
-Grenade/Reverse Grenade [Grab him or throw turnip]
-C4/Reverse C4 [Make sure you avoid the C4 and see what he will do next, and punish accordingly]
If you pressure his shield with properly spaced dairs while you float at a certain distance, you will limit his options, because:
-He doesn't have enough time for jumping out of shield and attacking with an aerial, because his aerials have a long startup.
-Even if he has a grenade on hand, Peach's kicks won't hit the grenade (maybe the explosion's hitbox will hit you though, so you need to watch out for that).
-Tilts and smashes won't work.
The only safe option he would have is to rolldodge, and if you keep on pressuring him, eventually he will be shieldstabbed, which can lead into a nasty combo. When he feels cornered, he will probably try to mortar slide to the other side of the stage, maybe try to outspace you with his tilts, pick a grenade, or jump (maybe with Up B), and you must exploit whatever he does and punish the best you can.
Can you use his nades against him effectively?
Use them only if you know how to work with grenades. If you don't, then stay out of their way.
How do you land the kill?
Be extremely patient with this. Don't freak out when you Fair Snake at 150% and he survives like it's nothing. Use your usual kill moves to get his stock, and use his explosions against him if you can. And of course, gimp him if you have the chance.
A cool way to kill Snake is if he places his dsmash and you grab him near it, you can grab release him into the dsmash. Another way is when he uses the C4 recovery, when he gets hits by the C4 you can footstool him to put him in a bad position. Works really well.
How do avoid being killed?
Be extremely careful of his Utilt and C4. They wreck Peach. I really don't know what else to say here. Just, play it safe and don't take risky decisions.
What's the most effective approach and attack on him?
Dair. And turnips.