Hi CW
The broader peaks might be ghosts. Strictly ghost peaks are substances that were introduced to the column in earlier runs than the one in which they appear at the detector.
Inject a series of samples and then inject clean solvent with the usual temperature programme. If the broad peaks are still there they are probably ghosts
Make a series of solvent injections, if the ghosts disappear or get smaller from run to run it confirms that they are due to carryover from previous samples.
To excorcise ghosts you need to clean up the samples (best option), or hold the column at the end of the programme to give everything a chance to elute.
Broad humps on the baseline can also be due to column bleed - check your carrier gas for water and air (change the purifier if you have one, install one if you do not). Baking the column will probably only make things worse.
Septum bleed can also give baseline humps, change the septum and check that septum purge really has flow through it (measure at the outlet).
Solvent effects can also give sharp peaks sitting on top of broad ones by distorting the profile of the injection analyte bands. Please post details of your solvent, inlet conditions, column dimensions and temperature programme. You mention a guard column - is this a "retention gap", is it coated or deactivated, and with what ?
Regards Peter