Apologies in advance for wall of text, you seem to want to play the same way I do so i got a lot of info to give you.
HQ:
1x Leman Russ Vanquisher - Pask. Lascannon, Multi-melta sponsons, camo netting, dozer blade. (255 points)
1x Leman Russ Executioner - Lascannon, plasma cannon sponsons, dozer blade (200 points)
1x Leman Russ Punisher - Lascannon, plasma sponsons, dozer blade, camo netting (200 points)
Personally I think these are best suited for 2 tanks maximum. And my personal prefrence is putting pask in the punisher. It is kind of a waste in the Vanquisher seeing as Pask grants preferred enemy a codex of your choice due to his warlord trait and that would mean the punisher is hitting on 3's rerolling ones anyways, the twin linking doesn't seem all that useful. So my suggestion might be Pask in punisher with melta sponsoons and hull heavy bolter with the Executioner. then do the vanquisher in it's own unit as a heavy support choice. The reason is that a punisher and executioner with full plasma is a lot of overkill. Since you are new one of the things that i have learned is that you don't want to waste firepower. and you would be. throwing doen 7 in total plasma cannons small blasts then the 20 shots from the punnisher barrel won't leave anything standing, but could also take down 2 separate units instead of the one you where able to.
Troops:
10x Veterans - 1x heavy flamer, grenadier doctrine
Chimera dedicated transport - dozer blade (155 points)
10x Veterans - 1x heavy flamer, grenadier doctrine
Chimera dedicated transport - dozer blade (155 points)
10x Veterans - 1x heavy flamer, grenadier doctrine
Chimera dedicated transport - dozer blade (155 points)
I highly recommend dropping grenadiers in favor for another special weapon in the squad. You might want to make 1 or 2 of these squads use double melta guns so you can crack tougher armor more reliabley (in my list i have 2 squads in chimeras with double melta and they preform great.) The reason to not take the grenadiers is that due to your low number of infantry the 4+ isn't really going to save them since all anti infantry weapons will be directed at them when they are outside of the chimeras.
Fast Attack:
1x Vendetta - heavy bolter sponsons (190 points)
1x Vendetta - heavy bolter sponsons (190 points)
I haven't really used vendettas but from everything i have heard they are a good solid choice. though i might drop one of them for a wyvern or 2 (65 points of pure amazing power) then get a company command squad with special weapons (4x melta not a bad idea) to load up in the valkyrie in case you need something to bee killed and are having trouble getting to it.
So I run a similer list to you in that it is focused on armor more then boots on the ground so here is what i usually use at 1500:
Primary Combined Arms Detachment:
Astra Millitarium
HQ:
Tank Command Squad: Pask in Punnisher with Multi Melta Sponsons. hull heavy bolter and heavy Stubber
Demolisher with hull heavy flamer and dozer blade (we play a lot of places where i can fit one tank through some where but the other goes through difficult terrain)
Troops:
10 Vets with 2x Melta Guns in Chimera with hull heavy flamer and dozer blade
10 Vets with 2x Melta Guns in Chimera with hull heavy flamer and dozer blade
Heavy Support:
Wyvern
Hydra with hull heavy flamer
Secondary Combined Arms Detachment:
Millitarium Tempestus (only for the different orders)
HQ:
Commissar with plasma pistol (rides with command squad)
Scion Command squad with Plasma Pistol on the prime and 4x plasma guns in Taurox prime with Missile launchers and twin linked autocannon
Troop:
10 Scions with 2x Hot Shot Volley guns in Taurox Prime with Missile Launchers and twin-linked auto cannon
5 scions with 2x melta guns
5 Scions with 2x Melta guns.
The way this list works is it is perfect for close quarters fire fights. Move up the field and kill the enemy. the 2 5 man scion squads stay in reserve to deep strike next to vehicles that need to die while the chimera's and tanks move up field and the taurox find a good distance to provide supporting fire. The hydra has a heavy flamer so in that rare chance the enemy is without a skimmer, flyer, or flying monstrous creature it can still provide some good damage and the wyvern sits back and hammers enemy infantry till they are nothing but paste on the ground.
One last thing, I would suggest you start at 1000 points instead of 1500 since that is a bit smaller and will help you learn to play the game a bit better. But no matter what, Welcome to the hobby! NOW GET OUT THERE AND SLAY THE XENOS AND BURN THE HERETIC!!!