Sarna.net has a description of the different ages and a lot of fluff and lore to read if you want a better sense of what's going on.
Coming from the BattleTech video game, 3025 is the right era for you to start in, and its also a good introduction to the tabletop as there isn't too much extra equipment to worry about.
There isn't anything 'bad' about most of the later eras per se, but basically as time went on and new eras were released, the developers felt compelled to introduce all sort of new technology along the way, while also trying to balance it against the existing technology rather then declaring some things obsolete to the setting. This leads to a lot more that you need to manage - take Autocannons for example. There are one type in 3025 (3 if you count the 2 LosTech models, the Ultra AC/5 and the LB-10X). By 3087, there are regular, light, ultra (full range), LB/X (full range), rotary assault cannons (Ultra++), caseless, hypervelocity, and rifles (proto-autocannons). Lasers, gauss weapons and missiles are equally a mess.
The one exception is the Dark Ages (3130+), but that's more due to WizKids fucking up the setting.
For a brief and somewhat biased history...
Around 2001, FASA, the original owners and creators of BattleTech content folded, and the BattleTech IP was bought by WizKids. They split it into BattleTech classic and Dark Ages. The setting had just wrapped up the FedCom Civil War era, and Dark Ages jumped a 100 years into the future.
Dark Ages was a shitshow, mostly because they decided that in a game about big, stompy robots fighting each other, what you needed a lot less of was big, stompy robots. The lore was equally stunningly stupid, where the mystical Devlin Stone managed to convince every faction, everywhere to dismantle their BattleMechs and founded the Republic of the Sphere. But now that
Jesus Devlin has disappeared, chaos has descended and everyone has started fighting each other again. Only the best they can manage for 'Mechs are jury-rigged industrial 'Mechs with weapons crudely strapped on.
This went about as well as you could expect. Personally, I left the fandom in disgust and didn't come back until a few years ago.
Anyway, in 2007, the split licenses were both acquired by InMediaRes, which merged them back together and started backfilling what happened between the end of the FedCom Civil War and the Dark Ages. They fixed a lot of the derp of the Dark Ages 'lore' and fleshed out what was vaguely referred to as a Jihad that led to the Dark Ages.