Feat advice

I've just started playing 5.5 ed (having skipped 5th ed completely) and am wondering what people think about feats versus just getting the ability score increases for monks
My monk was created with the standard array and started with 16 dex and wis, 13 cha, 12 str, 10 int 8 cha 
I'm not sure whether it's better just to bump dex and wisdom to get, hit, damage, AC and save DCs for abilities up or whether it's worth picking up a feat or two

Grappler seems tempting in theory, otoh 4 ability score improvements lets dex and wisdom both hit 20
1 feat means they don't (if I picked a feat that boosted either dex or wis I'm probably then get ability score improvement with 1 point in that ability score and 1 in con for the extra HP)
2 feats likely gives a max of 20 in dex, 18 in wis and no other scores increased
So dropping a point of AC and reducing the DC on abilities

What feats have people found worthwhile picking up for monks? 

My disclaimer is I personally would never play a monk with less then two rolled +16.  That allows your background to get your start with at least an 18.  I prefer farmer as a monk background as you boost both CON & Wisdom and get the feat to give you additional HP.   Monk needs multiple high/decent abilities.   Therefore getting feats at +1 ability is OK because you don't need to boost anything.

If you start standard array I recommend doing the  +2 ASI.  

Feat wise, what is your subclass?  Your subclass might influence what ability you want to boost and what feat might be a decent assist?

As for grapple that is a good default feat, but is never my go to feat.

Do you know how high level the campaign will go? It can help to know how many you’re going to get. 

Theres no really perfect answer. Mathematically, monks would just want the asi to max out dex and wis. Which one to go first is a tough call. Both boost your ac, an important save and a number of valuable skills. Dex also helps to hit and damage while Wis makes it harder to resist your stunning strike. Of course, you have to hit before you can even attempt to stun, but either way the number of attacks you get, you’re likely to hit at least once.

All that said, I’ll give the unsatisfying answer of, what would be fun for you? Say at level 4, you narrow it down to either taking 2 points in dex or the speedy feat. One of these means you will hit a tiny bit more often (about 5%). The other gives you some options for what you can do on your turn. No matter which you pick, there will be times you wish you used the other. For me, as the years of playing this edition have worn on, I’ve become less and less worried about squeezing out every last +1 I can find. Feats let you do some more interesting stuff, which is what I’ve found more fun, but that doesn’t mean you will.

On the topic, I will give a plug for speedy on a monk. At level 6, my base more is 55. I can get anywhere I want. And once I start running up walls, the extra movement will be really nice. Also disadvantage on OAs means I can flurry and still run away with needing to BA disengage. It’s been really fun. Granted, I started with an odd number in dex, mostly so I could take a feat.

And I have to respectfully disagree with the above poster. My standard array monk started with a 17 dex and 14 wis and is doing just fine. 

I went Scribe background so I could get the base array Dex and Wis both to 16, as well as getting Perception as a skill, skilled as the feat and Tough as the bonus feat for a human

Warrior of Shadow as the subclass

Echoing support for ASIs for this Monk. Monks are just so dependent on their DEX & WIS for all their things. I'm playing one now. So while it hurts to forgo the customization that feats give you, these stats really help you apply all the cool Monk stuff you already have. One way of thinking of is that kinda that those features are the "feats" you're choosing, since 2024 Monks have a fair amount of cool stuff they can do better now. They just need stats to support them - to land your Stuns more and any of your Shadow moves.

Your background and starting feats sound solid. As for Grappler, I'd say don't sweat it. I have that on mine, and it's definitely a good fit for Monks, but there have been stretches where I can't land a Grapple (since the enemy can choose either STR or DEX save), so it has zero impact then. Stunning Strike, however, is always there if you have the Focus Points. And you get a little something even if you don't land it. 

Beyond that, as the campaign goes on, you could feel out your DM to see if there are any items or perhaps homebrew things that could come your way that could impact that? There are very rare items that bump your stats, among other things. Mainly, I'd play it for a bit, see what you think is lacking and communicate that to your DM. Like if your CON is low like 14 or less, the Amulet of Health would be nice jump to 19. Dunno. There's stuff out there for you.

Getting the feats for fey or shawdowfell are useful as well.

The key is, what do you actually want?  Better ability scores or something fun/useful/???

No clear answer. Both ASI and Feats have benifits. Choose what the group needs most. That’s my response to your question.