In regards of the fleet would the order be
1 battle barge
4-6 battle ships
9-12 strike cruisers
No Rapid Strike Vessels? Given that Astartes often send out small (squad-scale) strike forces, individual vessels like the Gladius - frigates & destroyers - are quite useful. Not to mention their value as escort craft in a major fleet engagement.
A solitary battle barge as flagship is fair enough - a battle barge normally carries ~ 3 companies, but in this case I would expect it to carry the first company plus 'chapter support' elements - the armoury, librarius, reclusiam and apothecarion - the heads of which the Chapter Master would expect to be 'on hand' to confer with, rather than another couple of battle companies.
A strike cruiser for each other company makes sense, allowing them to operate independently, and one or two 'fleet asset' cruisers to support fleet actions without risking a line company in the process (or for a company to transfer onto if their cruiser gets shot up badly in a planetary assault) are also a sensible precaution.
The presence of so many battleships is an interesting one, though. Technically the Astartes aren't supposed to have ships designed purely for fleet combat (although many do, and fleet based chapters unsurprisingly ignore that rule more readily than most), but having 1-2 squadrons of the heaviest ships of the line in the Imperium is a bloody impressive achievement - that's more battleships than are generally present in a Sector Battlefleet of the Imperial Navy.
What's the reasoning behind so many heavies, especially given the lack of an associated escort screen?
A fleet-based Chapter might also find a number of ordinary unarmed freighters useful, depending on how often they have a chance to resupply.
There would definitely be some freighters, tankers and possibly Mechanicus Forge Ships assigned to the chapter - but Astartes being Astartes I'd expect them to be armed. 'Armed Freighters' still aren't a match for a proper destroyer, but they're still a far better idea to take into a warzone (and to perform shuttle runs between a warzone and the nearest Forge World) than the normal stuff a Chartist Captain might expect to command.