Which job would you take- one that is more (ingenious,gainful) right now or one that pays small salary but offers a chance for valuable training?

Gainful?
We were pleasantly surprised to see that she completed the difficult task we had given her with neatness and (irk,dispatch).
dispatch?

As soon as she took over the office of Mayor, she (besieged.dispatched) by dozens of people eager to get city jobs.
Besieged?
I will never (recede,forsake) the people who helped me in my hour of need.
(Famished,Compressed) for a chance to see her work in print the young writer begged the magazine editor to publish her story.
Famished?

For the recede and forsake question my answer is forsake

You're on a roll! All are correct. :-)

Famished means extremely hungry or starving. In the given sentence, it is used metaphorically to convey the writer's strong desire or hunger to see her work in print. The young writer is longing for the opportunity to have her story published.