I can't draw, so please vote on the design itself. Fonts and sizing need refinement, but what I'm pitching here is the overall layout and information that would be included in the list view. The top and bottom bars are placeholder (I know it doesn't include skills).
This is the scaling for 4:3 resolutions. Under wider resolutions such (16:9) the currently selected mech will take up any extra space on the right hand side. The user will be able to spin the mech.

Clicking the categories on the left works in two ways. Clicking on the text box selects that category and clears all others, while clicking on the check mark will add that category to the current selections. Mechs can be starred and added to the favourites list.
Clicking strip mech opens the prompt asking whether they want to strip mech components, modules and or cockpit items. This allows faster engine / module swapping as you no longer need to configure the mech first.
The search field allows users to search mech's by name and chassis type. So typing "Jager" will return all Jagermech variants and any mech which contains Jager in it's name (eg it would return a BlackJack "MiniJager"). The modules tick box changes the search function to instead search for mech's with the named module, so searching "Radar" would return all mech's equipped with Radar Deprivation.