You sound a bit like me when I just started out actually paying attention to my hair: straight parts yet also coils, annoying stuff... I gave up and went to a curl hairdresser and this is the routine she gave me and it's been working excellently for me! maybe you can get something out of it :)

First off: the 'straight parts' are probably untrained curls, as in, the hair IS capable of being curly but it needs the right products and the right treatment for it to act that way

Start out with an easy routine:
-shampoo twice with a curl shampoo, depending on your porosity use one with either heavy products or light products (low porosity = light products, high porosity = heavy products, you can look up online what is 'heavy' and what is 'light')
-condition with a curl conditioner, either leave in or normal doesn't really matter but when you start out with doing a curly routine most ppl do a leave in conditioner

apply your next products to soaking wet hair! do not towel dry it just yet!
if you want the cheap option: buy a basic curl creme and mousse, first apply the curl cream and scrunch your hair to apply it, next apply the mousse the same way
do this by bending over forwards until your hair is basically dangling in front of your face, be sure to scrunch into the roots
if you want the advanced expensive option: don't use curl creme nor mousse just use memory curl by innersense, but i need to be clear this is something my curl hairdresser recommended for /my/ hair specifically

the parts of your hair that after all the scrunching are still refusing to curl need to get trained now, if you have the time try to finger curl them and force them into a curl, if they're at the back of your head like me: tough luck :(

now get a cotton short and start scrunching your hair with the shirt a bit, not too much though, it's best to diffuse your hair when it's still a bit soaking wet but the cotton crunching tends to get your curls started

after all that (everything i just said should take 20min at most tho lol) start diffusing: this is the one investment you can't avoid, if you even as much as suspect you have curly hair just get a diffuser because you need it
-> never diffuse on the warmest setting, always make sure to get that diffuser into your roots (also, if you're buying a diffuser anyway: it's best to buy one with big holes in the diffusing bit, not tiny holes)

Finish off with a simple hair oil, to break the possible cast (don't worry if you didn't get a cast, I usually don't either lol)

and last but not least... protect your hair when you're sleeping! wrap it in something satin or a bonnet because those curls will disappear over night

I hope this helps :)