Taking guaifenesen and dextromethorphan (Mucinex DM) with acetaminophen (Tylenol) should not pose a risk of drug-drug interactions, since the metabolism (clearance) of these products do not directly interfere with each other:
Use as expectorant (thins mucus to make cough productive)
Metabolized via hydrolysis: Unknown if metabolism via liver enzyme cytochrome P450 (CYP450)
Use as a cough suppressant (anti-tussive) and pseudobulbar affect (uncontrolled crying/laughing)
Metabolized via liver, CYP450 2D6
Use to reduce fever and pain
Metabolized via liver, CYP450 2E1
The main dangers in these medications have to do with excessive concentration of the drug in your body, i.e. overdosing.
Overdosing on dextromethorphan causes breathing problems including no breathing, blurred vision, coma, hallucinations, gastrointestinal spasms (see Dextromethorphan overdose: MedlinePlus Medical Encyclopedia).
Overdosing on acetaminophen causes liver damage serious enough to require transplantation or result in death. You should not take more than 4 grams or 4000 mg per day. Brand name Tylenol comes in doses of 500mg each pill or caplet, which means you should not take more than 8 pills or caplets per day. If you take 2 pills or caplets each dose, you can only take 4 two-pill doses each day to stay on the safer side of liver damage.
Fortunately, guaifenesin toxicity is relatively low, but doses for an adult should not exceed 2400mg per day.
Mucinex DM comes in “regular” and “maximum” strength. Regular strength contains 30mg dextromethorphan hydrogen bromide (HBR) and 600 mg guaifenesin, which you can take 1 or 2 pills (2 pills yield 60mg dextromethorphan 1200mg guaifenesin) every 12 hours. Maximum strength contains 60 mg dextromethorphan and 1200mg guaifenesin, which you can take 1 tablet every 12 hours.
Source: Cough & Chest Congestion Medicine | Mucinex®
You can calculate which is cheaper, by buying either maximum strength and taking 1 pill every 12 hours, or regular strength but taking 2 pills every 12 hours. People tend to prefer swallowing 1 pill versus 2 or more, so less pills per dose is better for patient compliance.