Without any information about how you're going about things, there's only generic information I can give:

1) Pay attention to stats and proficiencies.

Make sure your characters are using weapons they're proficient with and have the right stats for them. Melee weapons need Str with Finesse weapons being able to use Dex. Ranged weapons need Dex. Each caster's spells have their own stat (Cleric uses Wis, Warlock uses Chr, Wizard uses Int, Bard uses Chr, Sorcerer uses Chr, Druid uses Wis)

Also, make sure to respec Shadowheart if you're using her, to adjust her stats into something not awful. Give her either some decent Str or decent Dex and a suitable weapon that fits the option you chose so she can actually attack things.

2) Dex and Con are your friends.

These stats are pretty valuable to have. Dex increases your initiative rolls (Making it more likely you act first in combat) and your AC (So long as you're not wearing Heavy Armour). Con provides health and helps with Concentration checks.

3) Concentrate!

Most spell capable classes have at least 1 useful Concentration spell. Which is well worth utilizing as such persistent spells can provide good bang for your buck in terms of spell usage. Spells that can make your opponents weaker, make your allies stronger or outright deal massive damage in an area are always great.

In regards to some of the points you raise:

Originally Posted by Super Fun Happy
Wondering if I need to buy my equipment in order to get stronger as I haven't been doing it

Buying equipment isn't necessary. Especially during Act 1 where there's not a great deal of worthwhile equipment (Off the top of my head, there's the shortbow from the gnome in the Grove that gives advantage vs Monsters, the Pike in the Goblin Camp if you're using a throw build character, the ring in the Underdark that applies +2 acid damage to attacks and the staff in the Underdark that gives +1 spell DC)

In Acts 2 and 3 there are much more valuable items available to purchase which are definitely worth acquiring.

In Act 1 most of the best stuff is simply found on enemies or given as quest rewards. Though, do check out the vendors to see if any item seems like it'd be useful for one of your characters. Gold is not a rare resource once you get a run going so you don't need to hoard it.

Originally Posted by Super Fun Happy
Currently have a level 4 Monk and still in Act 1 and manage to save the grove. I've done a bit of research on the unarmed monk and I am suppose to multiclass to fighter/rogue but I am looking for a build that can be useful straight off the bat instead of waiting for more levels.

Unarmed Monk is fine to start with. It's not particularly item dependent (Especially given you don't need melee weapons), though it is pretty crucial you have the stats for your build (High Str if going Tavern Brawler or high Dex if not)

I know many min/max builds will dump Str but still go Tavern Brawler because they rely on using Elixirs to set their Str to a high value. If you're not doing this, you'd want to raise your Str.

As far as multiclassing goes, Unarmed Monk doesn't need to (Or want to) multiclass until after level 6 because Manifestations are what super juice your fists into the strongest weapons in the entire game (Provided you have the Wis to back it up).

One thing I'll point out, is level 5 is a pretty significant powerspike for characters. Since it's when Martial classes get their second attack and Caster classes get an extra damage die on their Cantrips which significantly increases the damage you're able to do.