Here's what to expect from the games I design. I would expect that these will change somewhat over time, but for now...
1) Theme and mechanisms are important, and a game design can start with either, but what is key is creating the desired "experience": feelings, emotions, etc. For example, for Pocket Landship, my desired experience or feeling for the player is: desperation, and a feeling that not everything is under the player's control ("fog of war"). For 12 Patrols, I wanted a puzzly feel similar to Mark Tuck's excellent Orchard.
Some designers will say they are "theme first", some will say "mechanisms first". I guess I would say I am "experience first".
2) Give the player meaningful choices. Avoid experiences where the game is "on rails" where the player is just moving pieces around.
2a) Before the game: Set-up customization, enough content for replayability variety,
2b) During the game: Meaningful decisions, but not too many.
3) Low rules overhead. Design a game that is relatively easy to get to the table and start playing, without the need to consult How to Play videos or other online resources. I don't want players to have to spend a lot of time re-learning a game if they don't play it for a week or a month. So, in general, my game designs will be somewhat simple for this reason. Sometimes, this can result in a classic or retro feel game, but I am OK with that.
4) Quick-ish set-up. Again, get the game playing quickly. This typically means avoiding or minimizing sequencing cards in a deck, placing dozens of meeples/cubes/dice on the board.
A great example of this is 51st State. Game set-up and ready to go in 2 minutes or less.
5) Multiple paths to victory. There may be only a single win condition, but can I get there by using different strategies? For example, in Pocket Landship, the player can play aggressive focusing on attacks, or play defensive focusing on repairs. Both paths should be able to lead to victories.
6) Logical graphic design. Good graphic design can re-inforce 3) low rules overhead, and 4) quick-ish set-up. Expedition:Northwest Passage, for example, has the best player boards I have seen in a game, they convey so much information, they act as a player reference card as well. And, in Pocket Landship, all enemy cards are laid out in landscape, all player cards in portrait orientation. This makes it easy to identify and separate the cards.
7) If dice are rolled, roll dice (not a single die). This is just sort of a personal pet peeve. I don't enjoy rolling a single D6 die. It just feels unlucky, cold, and sterile to me. Rolling 2, 3, or 10 D6 dice is great. Rolling a single D12 or D20 die doesn't bother me quite as much, but I would still prefer to roll multiple dice at a time.
So, in some of my designs were I just need the result of a single die, I will have the player roll 3 dice and use the middle (or upper or lower) value.
8) Small-ish box games can be elegant. I am not looking to create "table hogs". I appreciate the elegance of a small box game. Tying in with #9, I don't want to cover game design issues by throwing more stuff into the design.
9) There is a fine line between a "hook" and a "gimmick". A hook is something that grabs you: a cool mechanism, maybe a cool theme, a cool component, etc. Nothing wrong with that, but the core gameplay needs to be engaging and shouldn't depend on the "hook" to keep players interested. I think there is some elegance to engaging games that are relatively low component count.
Here they are again, without details:
1) Theme and mechanisms are important, and a game design can start with either, but what is key is creating the desired "experience": feelings, emotions, etc.
2) Give the player meaningful choices.
3) Low rules overhead.
4) Quick-ish set-up.
5) Multiple paths to victory.
6) Logical graphic design.
7) If dice are rolled, roll dice (not a single die).
8) Small-ish box games can be elegant.
9) There is a fine line between a "hook" and a "gimmick".