Incense is a religious tool that spans many religions. The ancient Hellenes used it strictly as an offering to the Theoi; it was not used to set the mood, or because it made the oikos smell nice. It was a sacred offering that carried its sweet smell up to Olympos. From the Orphic Hymns, we know what types of incense a select portion of the ancient Hellenes sacrificed. I'll go through the list of incenses used in the Orphic Hymns today.

Aromatic herbs (ἀρώματα): aromatics are any woods, plants, or flowers which release a pleasant odor when burned. Examples are bay-leaf, chamomile, chrysanthemum, jasmine flowers, laurel, lavender, myrtle,  rose, sandalwood, verbana, etc. The Theoi who were offered aromatics: Adonis; Astraios; Athena; Ceralian Mother; Dionysos Trietericus; Eros; Erinyes; the Fates; Morpheus; Hera; Hestia; the Horai; Leukothea; Melinoe; the Nereids; Nymphs; Okeanos; Perikionios; Physis; Rhea; Sabazios; and Selene.

Frankincense (λίβανον): frankincense is tapped from the Boswellia sacra tree. The bark is stripped off, and the tree 'bleeds' tears of frankincense, which are allowed to harden before being cut off. There is great variety in quality--color, purity, aroma, age, and shape--and, thus, in price. Generally speaking, the more opaque resins are the best quality. Theoi who were offered frankincense: Ares; Boreas; Corybas; the Kourêtes; Dikaiosynê; Dike; Fortune; Helios (+ manna); Hēphaistos (+ manna); Herakles; Hermes; Mnemosyne; the Muses; Notos; Ouranos; Tethys; Themis; the Titans; Zephyros; and Zeus (+ manna).

Manna (μάννᾰ): we already discussed manna (and it's ability to singe your eyebrows off) before. The working theory is that manna is powdered frankincense. The Theoi who were offered manna: Apollon; Artemis; Astrapaios Zeus; Eos;  Erinyes (+ storax); Genius; Helios (+ frankincense); Hēphaistos (+ frankincense); Hygeia; Liknites Dionysos; Nike; Palaimon; Silenos, Satyros, and the Bacchai; Thalassa; and Thanathos.

Myrrh (σμύρναν): myrrh is harvested in the same way frankinsence is, and is commonly harvested from the species Commiphora myrrha. Myrrh gum is waxy, and coagulates quickly. It becomes rock hard very fast, and becomes glossy. The gum is yellowish, and may be either clear or opaque. It darkens deeply as it ages, and white streaks emerge. The Theoi who were offered myrrh: the Nephelai; Leto; Nereus; Poseidon; the Protogonos.

Storax (στύρακα): the word 'storax' is an alteration of the Late Latin styrax.  In the Orphic Hymns, it is called 'sturaka' (στύρακα). If you buy storax, today, you will find gum from the Liquidamber styraciflua. This was not the tree ancient storax was harvested from. You may also find the powdered bark of Storax calamitos (black styrax)--with or without vanilla added--marketed as storax (and incorrectly identified as Styrax officinalis). The modern benzoin, from the Styrax genus, comes closest to the storax of ancient times--specifically 'Styrax benzoin'. The Theoi who were offered storax: Demeter; Dionysos; Erinyes (+ manna); The Graces; Hermes Chthonios; Hippa; Kronos; Misa; Proteus; Prothyrea; Semele; and Zeus.

There are a few others who are mentioned once or twice. I will list them below:
Et Varia (Various Odours, ποικίλα): 'Mother of the Gods' (Rhea), Pan
Grains (no beans): Gaea
Poppy (mækonos): Hypnos
Saffron (crokon, κρόκον): Ether
Torches (Firebrands, δαλούς): Nix

Buying all of these is pretty expensive, but you don't need to use much to get a lot of fragrance out of them. If you don't buy the high quality incenses, you should be able to buy a small reserve of all of these for around fifty euros, less, if you find a bargain. Burning the incense is another matter entirely. On a coal is the preferred method, but this involves a lot of smoke and clean-up. For small offerings, I suggest a simple teaspoon with one or two tears, heated over (Hestia's) flame, or simply lighting the aromatics. For large offerings, the ethanol I use for my libations works well; add the tears or aromatics to the edges of the ethanol, where they can catch flame, and they will release their scent. If you have a fire going, you can simply toss the tears or aromatics in.

Incense was--and is--a precious sacrifice. Few could afford all of these incenses back in the day, so don't feel bad if you can't either, or can only afford to give a little. Then again, it should be a sacrifice; if you can afford to buy all these incenses in bulk, it's hardly a sacrifice to offer one or two tears. Make it count for your life, and your wallet. Make it count for the Theoi.