As someone who considered Ken Smith a friend who taught me much about chess and who is responsible for motivating me to study endgames (offers of books for accomplishments finally coerced me to not concentrate so much on openings) I tend to bristle slightly when it isn't called the Smith-Morra Gambit. He wrote at least 9 books on it, many articles, and he played it often.

It's more commonly called the Morra Gambit than the Smith-Morra Gambit, and also never called just the Smith Gambit, so I think the Morra part is definetely more important than the Smith part And with the recent release of The Modern Morra Gambit by Hannes Langrock, you could also call it the Langrock Gambit.

But if you insist:
1. e4
...
- Against 1... c5
...
- - Smith-Morra Gambit

2. Nf3 what is there to worry about!!?

(but I am considering a dabble with 2.Nc3)

Giuoco Piano, Grunfeld Defence, and Ruy Lopez.

I nearly always play c4 - The English - as white.
Against e4, I'm purely a Caro-Kann player. I especially enjoy playing against the Advanced in the Caro. I always reply 3...c5 against the Caro Advanced.
Against d4, I exclusively play the King's Indian Defence. I love it! Especially playing against the Saemisch.

at the moment the openings that have most occured in my games have been Budapest Gambit with 3...Ng4 (opposed to the Ne4 line)
Sicilian Dragon with 10...Qa5
and last but not least Danish Gambit which suprisingly most my opponents play poorly against!

White
Ruy Lopez
Sicilian defense
- 'Chekhover' variation against 2. ... d6
- Rossolimo variation against 2. ... Nc6 (sometimes transposing)
French defense
- Boguljubow variation against the Winawer variation (1. e4 e6 2. d4 d5 3. Nc3 Bb4 4. e5 c5 5. Bd2)
- The main line in the Classical (1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 Be7 5. Bxe7) or the Alekhine-Chatard attack with 5. h4.

Black
1. e4 e5
- Modern Steinitz defense in the Ruy Lopez
- Two Knights defense, Fritz variation against the 3. Bc4 stuff
- Falkbeer Countergambit, Nimzowitsch variation against the King's Gambit
1. d4 Nf6
- Nimzo-Indian defense if 1. d4 Nf6 2. c4 e6 3. Nc3
- Queen's Indian defense against most of the other stuff.
Against the miscellaneous openings I'll allow transposition to the above or just setup an all-purpose defense (c5-d5-e6-Nc6-Nf6 etc).

Actually, that'll be my reportoire at this point. I'll throw in the Caro-Kann, Alekhine defense, Dutch defense (and variations) and the Kings Gambit every once in a while though. I actually quite like the effect 1. ... f5 has against other first moves than 1. e4 and 1. d4.

What's that?

Yeah, I get that more often than not. I've heard it being called no-name opening before, I generally refer to it as Qxd4-Sicilian myself.
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Qxd4

Usually continuing like this:
4. ... Nc6 5. Bb5 Bd7 6. Bxc6 Bxc6 7. Nc3 Nf6 8. Bg5 e6 9. 0-0-0 Be7;

Here I chose between either 10. Rhe1 with a later Qd2 (which I call the Tal-system) or 10. Qd3 (the Polgar-system)

I've had great results with it.

Like you said in your first post, that often transposes to the Bb5 sicilian. There's a better way for black though, which leads to a unique line (not in the Rossolimo opening) when black plays either 4... a6 or 4... Bd7. I think 4... Bd7 followed by 5... Nc6 is just good for black, because then white will have to move his queen again.