Joe is a great investigator, capable of both collecting Clues (The main way to advance and win the game) and handle enemies (The main obstacle the game throws at you). There's never a turn when Joe won't have anything to do and he's a great Solo player as well as a useful member of any party.

Role of the deck: Flex. He won't investigate as well as a specialized Seeker, nor fight as efficiently as a specialized Guardian, but he can hold his own in both roles. He can also heal a little bit.

Crack the Case and Logical Reasoning go in your regular deck (Crack the Case is too reliant on timing to be useful in your Hunch deck, and you want to hold onto Logical Reasoning to either heal Horror or deal with bad Terrors you draw).

Strategy

Piloting

Mulligan for either a Weapon asset or Dr. Milan Christopher (Depending on whether you plan on focusing more on enemies or clues).

The rest of your hand doesn't matter as much: your many skills should be enough to cover you until you have Hyperawareness and Physical Training down (Neither of those are fundamental, but once you have Milan and your weapon of choice out you don't need money, and Hyperawareness and Physical Training can help you with difficult tests).

Many of your skills let you draw cards upon Success, so you should be able to find what you need fairly quickly.

Practice Makes Perfect can target Take the Initiative if you want to play defensively, or Deduction and Perception on tests and Vicious Blow on tests if you'd rather aim for those extra Clues and Damages.

Hunch Deck

All the cards in your Hunch Deck can be played for free (Except Unsolved Case) and are often useful regardless of their timing. Working a Hunch and Scene of the Crime let you discover testless Clues for free (Especially good on Hard or Expert), Preposterous Sketches and No Stone Unturned let you look for what you need (Usually a new weapon, or maybe Hallowed Mirror for some healing) and finally Emergency Aid can clear some damage on you or your friends.

Mythos Phase

The Encounter Deck will often be rough on you, but with Logical Reasoning, a Soothing Melody or two and First Aid you should be able to survive despite some failed and tests. Remember Take the Initiative and Practice Makes Perfect.

Alternatives

If you want you could replace Physical Training and/or Hyperawareness with Fieldwork. If you do I'd trade Preposterous Sketches with Shortcut (extra movement is always nice, and you have enough drawing power anyway) and First Aid with Delay the Inevitable (which is fast, so no AoO, and it gives you another outlet for your money).

If you need more damage on your team feel free to replace Dr. Milan Christopher with Alice Luxley: Crack the Case should be enough to cover your money needs. I tend to prefer Dr. Milan Christopher over Alice Luxley because her ability needs some good timing with the Hunch deck (Scene of the Crime and Working a Hunch), or being willing to take an Attack of Opportunity, but she's still a viable option.

Solo-Play Changes

First Watch is invaluable in Multiplayer (It allows you to let your Mystic friend handle that pesky Frozen in Fear or Crypt Chill for you, and you can pay them back by dealing with their enemies or Damage-dealing treacheries), but it becomes useless in Solo, so for Solo games feel free to replace it with something else (I like Guts to survive the Encounter deck or deal with Will tests during scenarios).

Deductions have the same issue: they're amazing in Multiplayer, less so in Solo. For Solo replace them with something like Magnifying Glass.

Upgrades

Deduction and Vicious Blow (Both targeted by Practice Makes Perfect) are great. Timeworn Brand can easily replace your Enchanted Blades, or you can use Machetes if you can't spare the exp for the Brand. Hyperawareness could be replaced by Death • XIII. You could also go for Charisma and get some fancy allies (Joe has access to a good pool of allies, after all). Deciphered Reality can sometimes gather a lot of clues and in your Hunch Deck it's 2 resources cheaper. With all your drawing power Extensive Research could also be a great addition to the Hunch Deck, especially considering how once you have your assets down you don't need money that much. If you find yourself often in need of actions Pathfinder can help you with getting where you need to be faster (and works great with Fieldwork, which could replace Hyperawareness if you feel like it) and lets you use Scene of the Crime even with a clue at a connected location. And finally, if you're playing in a team Leadership could easily replace Inquiring Mind (+2/3 to an ally and 2/4 resources, plus it's a potential target for Practice Makes Perfect). Even in solo mode Leadership could be useful (it's still a "+1 , gain 2 resources on success").