How good is 1. e3 2. c4 as an opening for White? Afterward, developing the knight on b1 to c3, and developing the bishops too, it seems good. Castling is preferably done on opposite sides as well.
Overall, I wouldn't suggest it, especially for a beginner. There are better ways to fight for an advantage.
By playing e3 first, you are allowing your opponent to do almost whatever they like on their first move. Are you OK with them playing 1...d5? Is that going to prevent you from playing c4? If that's going to be a problem, you may want to play 1.c4 first instead (which is the much more reputable English opening.)
With a pawn on e3, your c1 bishop has limited scope. Perhaps you want to fianchetto it to b2? Otherwise, it's either stuck on d2 where it doesn't do much, or you need to play e4 to free it, which perhaps means that e3 was a waste of a tempo.
Castling on opposite sides seems like it's something you need to decide later - don't do it if you aren't in the right position. If your opponent castles kingside (which they usually do), then castling queenside means that you're putting your king on the c-file, behind a pawn you've moved two squares (and if you've fianchettoed the c1 bishop, the b-pawn has also moved.) Depending on what your opponent has been doing and how open the game has become, this may be a bad idea.
It’s difficult to assess how good a relatively unplayed opening like this when considered in isolation. However I feel it’s dominated by the English. I want to play 1.c4 first, as it's directly aggressive, and leaves the door open as to how I will develop the bishops. I am unlikely to play e4 for a while, as d4 can become weak, but I don’t need to play e3 yet.
The question then is: are there any risks in the English which mean I should play 1.e3 first? What countermove would mean I don’t want to play 2.c4, and play something else? Actually, no Black response to 1.c4 particularly alarms me: I feel ok to play in any of the 20 positions which Black returns to me after his first move.
Domination of one strategy by another is a simplifying concept in game theory, in the absence of complete analysis. So a sufficient answer to the question: “how good is 1.e3?” Is “not as good as 1.c4!” The Nakamuras of this world will continue to play with it occasionally, but not, I suspect, against the Karlsens of this world.
Compared to what?
I played e3 myself way back then - if you manage to lure your opponent into a reverse Sicilian, especially any sharp variation where the tempo makes the difference, it's fine.§ Otherwise, hard to say. You could take a look at the Lichess opening book on the analysis board: e4 has 33/42/25%, e3 33/27/39%. But note those stats might be extremely skewed (only 687 games for e3, maybe all by the same oddball who will never learn...)
§After 1.e3 e5 2.c4 Nf6 3.Nc3 d5 4.cxd5 the stats are already 50/31/18. Even a GM game is listed, you have one guess who played White, hint: begins with N and ends with akamura. ;-)