The only time you should resign from a job is if you have another good job you are moving on to. No, it does NOT look better on your resume, as some employers will try to con you into believing.
It sounds as though you left your unemployment to go to the job, and now due to performance or personality issues, the employer wants to get rid of you. Of course, you don't want to stay, either, but if you want to resume drawing your unemployment benefits, you'd better not "voluntarily quit" any job unless you have an excellent job related reason for doing so. (Like not getting paid, or being assaulted by your boss)
It should not do too much financial damage (tax wise) to your present employer if he terminates you for "performance issues," because you have not worked for him very long or received many wages which could be taxed. But many will try the quit or be fired thing, thinking they are being clever and I don't know, saving the tax payers money or something.
You will file to re-open your benefits, which will be monetarily based on the original claim you filed at the beginning of your benefit year. They will do a fact finding investigation of the circumstances under which you left.
What you need to say is that you did the job to the best of your abilities, but that it just did not work out, that this is what your employer told you, and that you were given this letter or separation notice (if he does give you one, though it's not necessary to have one to file for benefits). Within a few weeks, they will have an initial decision and hopefully you will be able to start drawing your benefits again.
Remember, dont' quit, don't resign, don't leave unless invited to do so. This makes the burden of proof that they had a valid misconduct reason to terminate you the employers responsibility if they want to stop you from receiving benefits. If you quit, you are always considered to have chosen to leave the job, and the reason you left had better be a very good job related one.