I'm going to presume we're talking about having a downloadable PDF akin to the free Battletech Quick-Start rules. If that's the case, I have to agree with most of what has been said so far. Just to reiterate the points and add a few others:
-The Introductory Alpha Strike Rules: This is a given and a must. It's the same amount of playable quality in rules when compared to the Battletech Quick-Start rules.
-Succession Wars Cards for the Introductory Box Set Mechs: Use the same variants from said box set's record sheets to provide familiarity and let players get a feel for how things convert and play differently.
-A Quick Reference Page of the most basic Alpha Strike Tables: TMM, Attack Rolls, Mech Crits, and the very few specials mentioned in the intro rules (CASE/II, ENE, HT, MEL, and OVL).
-Barebones Battletech Universe Lore akin to what's in Alpha Strike p. 142-153: You already include about as much lore and stories in the Battletech Quick Start Rules. For people without the introductory box set it also gives a feel for what's out there and what they'd want to play as.
-A Page with Other Pertinent Information and Products: MUL Link (along with a brief description of it's gloriousness), Battletech Main Site and Forums Links (given), a list of Catalyst Products (namely the lance packs and the intro set that this complements with descriptions), and an IWM link.
-A Page each of sample Rough, Woods, and basic Water terrain templates: They're all covered in the Introductory rules and three 8.5x11 pages worth of terrain is plenty for an introductory lance vs. lance or company vs. company game.
-The aforementioned printable ruler: Even with .5 inch margins you can get 70 inches (7"x10" in 3/4" wide strips with 1/4" spacing) onto one sheet which can then be cut out and laid together, taped, stapled, etc. That's also far more then anyone would actually need . . . so you have even more room to work with if necessary.
-A page of printable mech tokens for the cards in hex format: It might seem stupid, but not everyone downloading this will have the intro set (or their own minis), and it also matches the way the sample pictures for the rules are displayed. TRO images shrunk down onto a little hex with a bolded border over 50%, to indicate the firing arc/front, is all that's needed.
Now, if this were ever to be an actual purchasable supplement to the Introductory Box Set I'd make the following changes:
-Small printed pamphlet of the Introductory Rules.
-Nice color cardstock cards of the mechs from the Introductory Box Set in the same style as the Lance Packs (Succession Wars on one side and Clan Invasion on the other).
-Four Cards (one for each weight class) for mechs that aren't in the Introductory Box Set or Lance Packs (like the extra Lance Pack cards).
-A small Card Stock quick reference sheet of the aforementioned tables from the Introductory Rules.
-Some terrain templates, in the same quality as the hex-maps of the Introductory Box Set, for woods, rough terrain, and basic water.
-A 60" tailor's tape that's simple and of durable material.
This is a little bit of a pipe-dream, I know, but it'd still be Amazing if we could buy a supplement like this for the Introductory Box Set . . . if I could get this I'd buy a new Intro Set and one of these in a heartbeat.
