I am going to make a family chart so that anyone that wants to try to breed plants can, and they will know what has the best chances of breeding successfully based on the chart, and certain plants that will tie parts of the chart together.
Nepetoideae (we'll call this a "Group") includes 3 "Tribes" only 2 of which have many species to work with, but the third may come in handy for someone: Mentheae, Ocimeae & Elscholtzieae.
Mentheae:
Salvia (Sages)
Romarinus (Rosemary group)
Lepechinia (Pitcher's Sages)
Nepeta (Catnip group)
Dracophalum (Dragon's Head group)
Agastache (Giant Hyssop)
Origanum (Oreganos)
Thymus (Thymes)
Mentha (Mints)
Saturja (Summer Savory)
Clinopodium
Bystropogon
Pycnanthemum (Mountain Mints)
Monarda (Bee Balm)
Dicerandra
Conradina (False Rosemary)
ALL of those are EXTREMELY CLOSELY RELATED, here is their sister "tribe".
Ocimeae:
Lavandula (Lavenders)
Siphocranion
Isodon
Haceola
Hyptis (Bushmints)
Orthosiphon
Ocimum (Basils)
Plectranthus (Spurflowers)
Solenostemon (Coleus)
Then there are "Cousin" Tribes.
Scutellaroideae:
Holmskioldia (Chinese Hat Plant)
Scutellaria (Skullcaps)
Lamiodeae:
Pogostemon (related to all Lamiodeae)
Phlomis (Jerusalem Sage)
Lamium (Dead Nettle)
Leonorus
Marubium
Moluccella
Rydingia
Leonotis
Stachys (Betony or Hedgenettle)
Sideritis (Mountain Tea)
Stenogyne
Phyllostegia
That is it (as far as we have genetically) of the Nepetoideae, but that is not the end of the larger "mint" family. So more chart to come later.