Your existing pedals probably need a pedal spanner. Flat pedals mainly tend to just need an allen key.
Ideally, sealed bearings are the way to go but you will need to check on this.
Pedals are very personal and you will get lots of different suggestions. But I would suggest that you need to use them in conjunction with decent shoes with a grippy sole.
It’s possible that if you have larger than average feet, you would need a broader platform.
I started off with dmr’s but didn’t get on with them. Now use Straitlines but they will be dearer, unless there’s anything on the Classifieds.
On my singlespeed I use a different pedal – Funn Soljams and they should be within your budget.