If you could start with any non-legendary Pokémon (in its basic form, of course)...

[Maniacal Engineer]

Good question. Although Metagross is my favorite Pokemon, I wouldn't want to start with Beldum, as it is difficult to raise and would get completely walled by Ghosts until it evolves.

I'd probably start with an Eevee, because it is very versatile, and could evolve into whichever Pokemon best fits the rest of my team.

 

[Anime Psyclone]

Hm... Xurkitree. Or Kartana.

 

[SirOni]

Scraggy is a strong contender for me.

 

[DoctorWhy]

I'll also exclude all Pokemon which have been starters in the main series, in addition to legendaries.

Well, I know I would want this starter to evolve by friendship. Those tend to be my favorite evolution lines, because I feel even closer to the Pokemon. I think I would pick...

Riolu. Definitely Riolu. Lucario is one of my favorite Pokemon of all time.

Other close contenders include (still excluding actual starters): Eevee, Ralts, Nidoran (M), Phanpy, Spheal, Bagon, Shinx, Growlithe, Vulpix, and Drilbur

 

[Derpghost]

Sableye or Cubone(To evo into alolan marowak). I'm suckers for ghosts, and these two are my favorites.