First, there's a difference between tactical speed (eg. on the map), and strategic speed (eg. can you move assets in place either on their own, or buy carrier like DropShip or hauler?) Think of slow tanks like BA that way - low tactical speed usually, high tactical speed if they have an APC.
Second, the mission dictates the need. There's no perfect mix, so you're looking for flexibility.
Third, like most things, synergies are real - combinations can be more effective than the sum of their parts.
So let's consider very slow heavies - the Challenger, Zhukov, Pike, Alacorn etc. What are their strengths? High damage resistance, high damage output (usually). You need these when you
- want to stop someone taking X away
- want to take X away from someone
In the former case, low mobility - strategic or tactical - is less relevant. You know where X is, you park the tanks around it ;) In the latter, if you have strategic mobility, then you can bring your heavies to the edge of battle, and move your other forces around their speed. The 'turtles' claw their way through fire, doing as much damage as they can, ideally with other units covering their flanks & rears.
Not-quite-so-slow 4/6heavy tanks can't match a 'Mech for mobility, when jump-jets exist. But they do represent reasonably well protected firepower (not neglecting turret capability for all-round field of fire). So they make the core for a less intensive assault. Alternatively, they provide the rear cover for faster, more mobile units - either directly, or with indirect fire. They're also handy for a mauled battlegroup to fall back on.
The LRM & SRM carriers are special cases, with their low protection. The LRM carrier works more like the second category - they're supporters, who usually need hills to hide behind. The SRM carrier is a specialist mugger for urban terrain. I have a fondness for the laser carrier - 8 ML. I see them as urban renewal units - when you're facing dug-in infantry in prepared positions, use the conventional units to suppress the infantry, then have the laser carriers 'saw' their bunkers apart. So economical!
I try and come up with these uses in my combined-arms battalions. My Alliance Guards had lots of light & medium 'Mechs, accompanied by Manteuffels, Glorys, and Galleons. The Manteuffels were the "core of the assault", especially with two platoons of BA on board. The Glorys were the supporters, who provided a safe place to regroup on in case of trouble. The lighter units swept the area, kept an eye on flanks, and took advantage of opportunities.
My 2 (in this case) L-bills.
W.