From an ingame standpoint? Use whatever you want, they're all good as long as you do the overlevel >:D
Competitive viewpoint? Their final forms are all in NU, and aren't really that 'good'. Their prevolved are obviously in LC. Here's a quick overview
Rattata is an okay choice in LC. It's hidden ability 'Hustle (Physical moves do 50% more damage at the cost of 20% accuracy). and also it's other ability Guts (Increases attack by 50% when afflicted by status) gives it some offensive presence coupled with it's decent base 72 speed. However, it's horrible bulk still means good priority attacks will do a number on it, and support is required if you want to keep it alive. Not a bad choice in LC, go ahead and use it
Raticate is, personally an outclassed choice in NU. It faces competition from various other Guts users including Ursaring and Zangoose. The only thing it boasts that the other two can't is it's access to Sucker Punch, which is good priority albeit kinda unreliable due to it's reliance on the opponent attacking. Since Raticate functions in a similar role to Ursaring, etc. most teams which have a solid counter to those kinds, will be able to deal with our Rodent Friend. Yeah not really a good choice for NU I'd say
Due to its terrible stats, Sentret is one of the worst Pokemon to use in Little Cup.
Furret is fast and cute.
In a nutshell, don't use them.
Zigzagoon in LC has access to Belly Drum and Extremespeed. If you can pull it off, Zigzagoon becomes a complete monster. Use it if you think that you can pull it off.
The same holds true for Linoone in NU - Belly Drum + STAB extremespeed.
They both still have bad bulk, so Pokemon which have the ability to take a hit and dish it back suck for Linoone and Zigzagoon. Also, they're realllly predictable.
Bidoof actually has some use, if not alot in LC. Utilising Simple + Curse and a fair bit of team support, it might just make a sweep. :P Unfortunately, most fighting types can kill it and Pokemon like Frillish and Ferroseed wall it forever. I wouldn't use it but... if you have the team support and the guts, have fun xD
Bibarel. Bidoof has some use. Bibarel doesn't.
Bibarel is generally an unfortunate case. All three of its abilities are among the best in the game (Moody being banned for being too overpowered), but Bibarel simply lacks the stats and movepool to make good use of them.
Don't. Use. Bibarel.
Patrat isn't exactly a Pokemon one would look to for a slot on a team, mainly because of its very low stats. It has a decent physical movepool but it lacks the power and Speed to sweep effectively.
In most cases, don't even bother. But in Patrat's defense, it is a decent baton passer so if you're trying out a team with that, you could use it
Let's take an overdone concept, make it as ****** as possible, give it the creepiest eyes known to Pokemon, and release it into the world just to watch the Pokemon fandom squirm. ~Game Freak
Don't even try.
Not really sure on these two, being recent and all, but from what I've seen their stats are utterly horrid, but their hidden ability, Huge Power might give them some use. (Choice Scarf + Huge Power maybe?)