These naturally occurring, volatile aromatic compounds are found in the seeds, bark, stems, roots, flowers, and other parts of plants.
They tend to change quickly from their solid or liquid state to a gas at room temperature.
They are used for food preparation, beauty treatment, aromatherapy, and health-care practices.
They are produced several ways:
1. Distillation The most common way. Freshly picked plants are suspended over boiling water, and the steam pulls the oils out of the plant. The steam is rapidly cooled causing the water to condense out.
2. Expression - Pressing as in olive oil extraction.
3. Solvents - The plant is dissolved in a solvent such as benzene, hexane, or chlorure of methylene. The solvent, which has a low boiling point, is then evaporated off. Aromatherapists avoid oils produced this way because they worry that slight traces of the solvent remain.

Quality essential oils are 100 percent pure, "so a little bit goes a long way."
How Essential Oils Are Produced | HowStuffWorks.

Some things to check:
1. Is the Latin name of the plant provided so that you are sure you are getting the right essential oil? For example, there are several species of lavender.

2. Is there a statement about purity? You should be informed if it is not 100% essential oil (meaning, it has been altered or mixed with something else).

3. Is the cost comparable in comparison with other brands of the same essential oil? If it's really cheap, it probably isn't the real thing.

4. Is there information about organic growing or wildcrafting (gathering wild plants)? Most essential oils sold in the U.S. are not certified as to their organic status, but some European brands are.

Source: How Do I Determine the Quality of Essential Oils? | Taking Charge of Your Health & Wellbeing

For the most part you want therapeutic medicinal grade essential oils unless you are making perfume. As an example, Lavender perfume grade essential oil may only be distilled 15 minutes. Therapeutic grade may be distilled 1 ½ hours ensuring all the chemical constituents are present in the oil. Both are “Lavender oil” but the chemical content may not be the same and the therapeutic value you are looking for will definitely not be the same!
Source: The 'Ins and Outs' of Essential Oils by Someone who Knows

The label will sometimes contain chemical names.
Some e.g. "2-Methyl-6-methyleneoct-7-EN-2-OL" appear to be the chemical name of the oil itself.
Benzyl benzoate is a synthetic chemical used as a fragrance ingredient, artificial flavor, preservative, and solvent.
See Chemical of the Day - *Today's Chemical - SquareSpace.com
I couldn't find any reference as to the safety of these chemicals.

See:
What are the best essential oil brands? | EssentialOilHaven.com
Best Essential Oil Brands Reviews and Comparisons for 2017 | WellnessApliances.com Safe or Toxic? How Much Do You Know About Essential Oils? | Common Scents Mom says,
The Quality of Essential Oils | National Association for Holistic Aromatherapy
"When you’re using a truly pure product that has not been cut with other chemicals or distilled using solvents etc. they are very safe and effective – and honestly, amazing!."
The 'Ins and Outs' of Essential Oils by Someone who Knows

What each evokes
(Scents & Sensibility: Creating moods with aromas - The Morning Call)
Recomendations from Donna Wood, owner and principal designer of Stonewood Interior.

• Cedarwood - strength and centeredness
• Cinnamon - mental clarity - refreshing.
• Citrus family - Uplifting and cheery. Fresh and clean.
  That's why a lot of cleaners and polishes are lemon-scented.
• Clove - warm and comforting atmosphere.
• Ginger - warmth and strength.
• Lavender - soothing and calming effect. Sleep aid.
• Lemongrass - fresh, earthy scent that also can have a calming effect; Invigorating and inspiring.
• Spearmint, wintergreen and peppermint: Spearmint and wintergreen are said to make the home smell refreshing. People often associate peppermint with Christmas and happy times.
• Sweet basil - floral, spicy aroma is said to be energizing and uplifting.
• Vanilla - Joy and happiness. A study published in the journal, "Chemical Senses," said it elevated their mood. (Note: vanilla is not an essential oil.)