MegaMek is a freeware Java-based program that you can download and use to play BattleTech against bots or peoples. We are using the latest stable release, from this summer. It's a very strong build. They have supposedly been working on making the AI better, specifically the Princess Bot, and we'll lean on it as our foe.
Interested in MegaMek and other fun stuff?
MegaMek | an unofficial, online version of the Battletech board game
There are ongoing campaigns you can join via MekWars, you can design your own units on MegaMekLab and use MekHQ to track your company and take contracts and such.
I track our units on Excel spreadsheets, and there are some out there that have been fully tricked out in a variety of ways, dinging all of the rules for Dragoons ratings, repair, medical staff, and more. I use one for each company in our TOE. (Table of Organization and Equipment, a list of a military's full assets).
I personally use the not-free software called Heavy Metal, which is officially licensed. That's my software for making fighters, small craft, tanks, mechs, and more. It's not cheap, biut I like the quality it offers over free options, like Solaris Skunkworks.
http://www.heavymetalpro.com/