There are certain factors which are not mentioned here, which have a lion’s share in the final decision. It depends on what position the person presently is in.
For example, for a person who has made ZERO investment in skills and is stuck doing repetitive tasks, someone in his position should choose skills and entry level equipment over advertising (you cannot hone your skills or learn new ones unless you have the bare minimum equipment). Someone who does data-entry, VA type jobs should invest in skills, tutorials, get certified for better paying skills. No point in spending on advertising or buying professional equipment at this point. Just get basic equipment but invest heavily in skills.
Verdict : Skills
If someone has mediocre quality equipment already, then he should give preference to investing in a new skillset and buying new equipment over advertising. There’s no point advertising sub-standard quality work in a highly competitive world. Let the low paying-low demanding work trickle in naturally, commensurate with the quality of equipment and skill. A graphics designer who uses a normal consumer grade computer and 2D sketching software should definitely get a graphics card and invest in 3D wireframing software instead of wasting money advertising his 2D gigs. This will yield a much better ROI in the long run.
Verdict : Equipment
If someone has excellent quality equipment, they should invest all of it in advertisement to break even vis-a-vis the money they had earlier invested in the equipment. The reason they were able to afford this equipment was that they had the skills to pay for it. So they’re set as far as skills are concerned.
Verdict : Advertising
Ideally a successful freelancer/business goes through all three phases where they prioritize one over the other depending on where they stand. Advertising should always be the last stage of evolution. It’s only worth advertising if there’s something worth advertising.