I posted this in another thread, it might be of use to you!
Welcome to Battletech! This universe is massive and full of awesome fiction, designs, books, minis, and more!
To get started typically the Intro box set is your best bet but, that is Out of production and the new one isn't due until roughly 2nd quarter 2018 from what I've heard. Even if you get everything by then, like many of us, you might just be the intro box set at that time anyway for the minis.
Every player typically winds up with at least these basics: Minis, The base rulebook, hexboards/mats, and a record sheet program.
To start you will do best with Total Warfare, you are looking for the CGL copy as that will find you one of the most recent editions. It'll be in green print on the cover. This book includes all your basic mech rules and sets you up in the future IF you want to add armor, infantry, VTOLs, etc. to your game. A book has been/will be released called Battlemech manual that supposedly has all the Mech specific rules and that is it. You will have to compare prices and info vs value for yourself.
Next up are the actual minis. Ironwind Metals is the place to go for pewter minis. They look fantastic with minimal shaving of mold lines and sprues. Remember, Battlemechs are a representation of a mech controlling a hex, they are not all to scale, even though many are pretty close. Don't forget to get hex bases for your pewter minis! I would recommend using Loktite gel superglue (gray or black and blue squeeze bottle at any big store). You want to cut them all out, shave any excess pewter, score the joints with a utility knife, wash them with soap and warm water (removes mold release), then add a primer and paint. The next cool option is CGL's Lance packs. You get a full lance in each one and each one has at least 2 mechs that were in the out of production intro box. It's roughly 10 bucks for 4 plastic minis and they look pretty good.
This may be the most difficult to decide on. What to play on. You can find hexboards for sale on ebay and sometimes you will even find the mountains and canyons or cities and roads hexpacks for sale online. (The lakes and rivers is a unicorn find, I barely have the one i found). There are multiple sellers of hexmats you can unroll. As for terrain, hexpack terrain cutouts are fantastic but if you like 3D better, there are a few people that have good 3D terrain for sale, you can check out Battletech International on Facebook and find them a lot.
Finally, for a record sheet program, I highly recommend Solaris Skunk Werks. You will need java to run it. It already has most designs through 3085 and everything to build most mechs up to the current year in 3150. There is also a vehicle builder through them, soalris armor werks.
I am not sure how caught up you are to the fiction but the current year is 3150 starting from way back before the year 3000. There is a lot of cool stuff you can use in the current era that can play just as well with mechs from before the clan invasion in 3050. I would recommend looking at some cool mechs like the Gunsmith, Lament, Prefect, Malice from the current era. (There are minis for these 4).
You have a mountain of fiction you can read through as well. There are Mechwarrior, Battletech, and Mechwarrior: Dark Age novel series. Sourcebooks about factions and eras. Technical readouts (TROs) for every decade nearly. Sarna.net is the wiki of Battletech as well. If you have never played through a game I have a video series on Facebook called How to Play Battletech that breaks down the basics of using mechs, imperfect, but the only ones in detail like that.
If you have more questions, ask away!