From my experience and observations, it's generally easier to transition from a round-gauge aircraft to a glass cockpit. If instrument skills are developed solid in the round-gauge, then they are usually still solid in the glass. Instrument flying IMO is looking at the right place at the right time, which sounds simple, but in reality it relies on knowing many relationships, being able to estimate changes, set them on the attitude indicator, not have to look at certain instruments for significant portions of time, but look at them nonetheless. It's nice having everything right together on the glass display, but once you separate it out, such as for your first serious commercial job flying a metro liner or king air, many people tend to look around randomly and spend nearly equal amounts of time on each instrument, bouncing back and forth with no real structure. This doesn't usually cause huge issues when everything is working right, but more than once I've seen people lose control or fly into mountains in the simulator when an instrument fails, even during simple failures like having to use a backup round attitude indicator, which for those of us that learned on round gauges, there should be no excuse for.
There are specific ways when teaching instruments to build that structure, and while I won't say it's impossible to do with a glass cockpit, it's much more difficult, like trying to determine where the student is looking over a much smaller distance and whether it was a lack of understanding that led to an error or if an error was covered up by using another instrument in close proximity.
This is all very opinionated and you'll get lots of flight schools and others that have spent lots of money on glass cockpits telling you that you need to learn glass cockpits because that's what the airlines have and that's what they want. Most younger people are pretty tech savvy and this isn't much of an issue IMO. In fact, some of the FMS systems on some of these aircraft are very ancient in terms of programming and data-entry, like a computer from 1982, so I've seen that present more of a challenge to some young people in terms of the poor interface (that many people have adapted to). So I wouldn't worry about "learning glass", there's also a lot of different systems that present differently. Things are great if you are on a garmin 430 or basic G1000 and upgrade to a G3000+ suite in a learjet or something, there will be a lot of crossover, but go fly a collins pro-line and you'll be lost. Unfortunately, airliners are not all equipped with the same systems.
Time building is time building, you want to get hours as efficiently and cheaply as possible, while maintaining good training and proficiency.
There is absolutely nothing wrong with using a LSA aircraft or "glass" aircraft. You can become proficient in it and any checkride is about being proficient in the aircraft that you bring for the checkride. Whether it will provide the best training for instrument flight might involve some decisions on your part, but that too can absolutely be done.