My knowledge of bikes is limited so please bare with me I am still learning.

My derailleur broke off a few weeks ago, and my bike has sat idle while I figure out which type to replace it with, unfortunately I don't know about derailleurs & find them a little confusing. I'm looking for any assured answers before I buy anything.
I have a single chainring with 42 teeth
A 9 speed cassette 11-32
I have an old looking dura-ace lever system that is attached to the downtube

My bike in general is not expensive nor professional but I like it and I don't mind upgrading it when something breaks.

Any suggestions on a derailleur that would run nicely on these spec's are welcomed.

Thanks in advance.

Derailleurs are relatively fine tuned machines and as such are fussy to set up correctly.

Since you are very inexperienced at bike mechanics, I suggest you save yourself a lot of grief
and take your bike to a local bike shop. They will sell you a suitable derailleur, install it and adjust it
for you.

With a 32t large cog on your cassette, you'll want a MTB or "mountain" derailleur. Road derailleurs seldom allow you to use a cog this large.

Shimano MTB derailleurs commonly come with two different cage lengths, noted as "GS" or "SGS." Since you're using a single chainring, you can use either cage length. If you had to run a longer chain to accommodate a triple crankset with your wide range cassette, you wouldn't have the option of using the shorter ("GS") derailleur.

If you use friction shifting for the rear gears, you have a slightly wider range of derailleur choice, since the derailleur is simply moving the chain from cog to cog and doesn't need to be compatible with a particular mfr's indexed shifting. If you use indexed shifting, you'll want to stick with a Shimano derailleur to maintain the same cable pull ratio. However, some of the newest Shimano MTB derailleurs pull a different amount of cable and won't be compatible for indexed shifting with your shifter.

Here is a nice Shimano derailleur that won't break the bank and is compatible with your needs.