I think the advice given by Betawing is pretty sound. Now if your going for a fluffy list, Alpha Legion was still a very tactical hit and run force. Using lots of assault troops and jump packs. The dread seems kind of out of place a bit
For game effectiveness i would say the biggest problems i see is that your using a chapter master and stern guard. While a nice units for an army, they are very expensive at this point level. You MIGHT be able to get away with it with the right strat. Heres something along the lines of what i would use:
HQ:
Captain w/ JP, DW, PW - 155pts
This guy is a solid vanilla hq choice. cheaper then the chapter master and just as about as effective. Stick him with the assualt troops
Troops:
10 Tac Marines w/ PF, PG, ML, Rhino - 240ots
10 Tac Marines w/ PF, PG, ML, Rhino - 240ots
Betawing is right, plasma just isnt worth the risk, plus you wont be able to charge if close enough and want to fire it, but you seem stuck on them so i used them. The points could be better spent to give the speeders back their HBs or getting extra armour on the rhinos which i would also recommend, i just couldnt find the points for it. Lastly, you not liking MLs? thats just SMs man, i mean come on, you can't pass up that upgrade for that price. Even if you dont use it, you still getting the same amount of attacks as a normal marine since we apparently aren't cool enough to get a BP, Bolter and a dang CS like the CSMs.
Fast Attack:
7 Assault Marines w/ PF, Flamer - 171pts
Coupled with the Captain these guys should fare well if you just do a tank shuffle to shield them up to the line to charge. I just couldnt validate such an expensive unit as vanguards or sternguards at this point cost. for the same points you can get more assault marines. I don't usually run these guys short of 10 men, but at this point cost, shielding them correctly and the captain, they shouldnt do too bad. plus this just helps your fluff effect.
Landspeeder w/ MM - 60pts
Landspeeder w/ MM - 60pts
I always run these guys in pair or better, or else they just become rubble on the ground. Keeps in the "hit and run fluff" of the Alpha Legion and can provide some much needed anti-tank support.
Heavies:
Predator w/ Autocannon, TL-HBs sponsons - 85pts
Predator w/ Autocannon, TL-HBs sponsons - 85pts
Perfect for softening the lines before you guys get there and cheap for what they can do. Just all around good heavy support for effectiveness.
1096pts
There, with that list your list has some more meat, much needed support, a good dash of the fluff and a solid foundation to expand later on. Hope that helps somehow. Good luck and happy hunting!