Are you searching for a job?

It is asking about your last job, so the response should be in the past tense:

I bought a newspaper and fpund an interesting job advert for me, applied for and was offered the job.

It is usually easier to find a job at a temporary work agency but your pay tends to be lower.

(If you found the job in the newspaper, you do not need a headhunter.)

I'll buy (question asks for the past tense) a newspaper, I think that I'll find some interesting job advert for me.
The headhunter propose me a contract.
Usually it is easier to find a job in a temporary work agency but in that case your remuneration will be lower.

I'll buy a newspaper, I think that I might find some interesting job advertisement  ( or just "ad" ) for me.

The headhunter proposed me a contract. (better to say : I got a job through a headhunter)

Usually  it is easier to find a job in a temporary work agency but in that case your salary will be lower.

Really good!