Good Job! Follow this method to make a fresh install in few secs without losing anything.
-Rename wp-admin to wp-admin-old ; wp-includes to wp-includes-old
-Download the latest wordpress and upload the new folders: wp-admin and wp-includes
-Now remove *-old folders you earlier renamed.
-In your server/ftp, Inside wp-content folder, There are only two folders you need to back up or download them to your pc: uploads & themes.
-Those folders you downloaded to your pc scan them and if you found malware do not remove the actual files, but look for javascript/php codes injected. Sometimes you may find a file that is entirely malware code, just remove the entire file in that case.
-After this cleaning is done, remove all folders and files inside wp-content, and upload themes and uploads folders back to your ftp.
-If you find other malware codes in wp-config.php or wp-login.php <-- root files, again just look for the malware code and remove and done.