I have one bike in the family with Tourney stuff, my 11 year old daughter's 2015 Raleigh Alysa 1. I've been generally impressed with the value of this bike as a whole, and the Tourney stuff plays a part in that.

First, you did ask about "chainring size" and the rear derailleur -- most Tourney-equipped bikes are aimed at the entry level market, where riders generally prefer easy pedaling, and they often come with the 34T "Megarange" freewheels. A Tourney RD can easily handle a 34T large cog freewheel. You asked about chainring, though -- most will have a 28-38-48 triple on the front. Are you looking to install a larger chainring than 48T? The RD should be able to accommodate most anything within reason, as long as your chain is sized appropriately.

As far as how Tourney operates, I find it to be relatively durable stuff. My daughter hasn't broken anything on her bike, yet. It's fallen down on the drive side and there are war scrapes on the RD to prove it, but everything stays in alignment. I do like how Tourney is the only RD Shimano makes below some of their newer high end stuff that has a cable pulley on the back, so that you don't have to have a tight radius in cable housing. I think that type of arrangement can only help with shifting tension, etc. Maybe it's because Tourney is the only group that comes with twist shifters. I do not like the Tourney twist shifters (branded Revoshift). They seem to be durable, but they have relatively small gripping surfaces, and they can be difficult to use. The rubber surface is REALLY stippled, which can tear up the webbing of your hand if you shift a lot. I like Sram's (branded Gripshift) twist shifters much better at this price point.

Shifting, as others note, is not always super crisp, though it certainly works just fine. And it likely will work just fine for years and years. Her bike has the MF-TZ21 14-28 freewheel (not the 14-34 "Megarange") and a KMC Z7 chain. Upshifts and downshifts are executed quickly. There is sometimes some chain jump when upshifting (down the cassette) and there is sometimes some brief gnashing when downshifting (up the cassette), but some of that is user technique (shifting when pedaling slow or under load). I have better luck with it when I ride her bike.

The bikes I ride have somewhat better components than hers, but not by a long shot. My 2015 Trek has Acera, my 1997 Trek has STX (analagous to the base level Deore today), and my 1995 Motiv has Alivio. These all work a litter better than her Tourney in terms of refinement and smoothness, but they all also have trigger shifters. I think the Tourney components are let down somewhat by the Revoshift shifters. Put some nice triggers in front of a Tourney derailleur, and it'd probably shape up pretty nicely.