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I'm starting an ultramarines army with what I already have and what models I want (because I think they're cool)

HQ:
-Captain (join termies) Artificer Armor, Relic Blade
-Chaplain (join assault marines) Jump Pack

Elites:
-Dreadnought MM
-Terminator Squad (5) vanilla in Land Raider
-Sternguard Squad (6) 1 flamer in Razorback

Troops:
-Tactical Squad (10) LC/Flamer, Sergeant w/ PS
-Tactical Squad (10) LC/Flamer, Sergeant w/
-Tactical Squad (10) MM/Meltagun in Rhino

Fast Attack:
-Land Speeder assault cannon
-Assault Squad (10)

Heavy Support:
-Devastator Squad w/ 4x missile
-Devastator Squad w/ 2x PC & 2x HB
-Predator Squad w/ AC & LC side sponsons

What do you think?

First off, lose the chaplain. you can maybe justify the captain, but the chaplain w/assault squad will not do what you think it will. If you want to keep them for sentimental reasons, you can. Else I'd say lose those 400 points.
Tac squads have to have Rhinos or Drop pods. There is sadly no other option.
On that same track, Dev squads should be 5 man with either 4ML or 3ML/1LC. Lose the squad with PC & HB. That sternguard squad needs some combi-meltas or flamers, and those termies need an AC (maybe a CML).

What I see here is someone who bought AoBR, a battleforce, and some other stuff. That's very cool. But you'll have to accept that it won't be very competitive if you bring everything along

Simple things (changing the LCs for Missile Launchers) and giving the termie an AC/CML will help, as will upgrading some of those sternguards. The Land speeder, if you can manage it, should be MM/HF in my opinion.
You can maybe justify briniging in the assault squad, but they're a big target, and they aren't too resilient. Those two tac squads are going to need rhinos/drop pods. Marines can't footslog well, they'll be eaten alive. Might also be nice to give a HF to the dreadnought and maybe a drop pod.

I mean, it's up to you, but the tactical squads without rhinos are going to get annihilated. The dev squad w/PC/HB are also not as effective or helpful as the 4ML squad. In fact, they're kinda out of place. Either something will rush them (using cover) or they'll send something mean and tanky to kill them (as the PC is not that effective anti-tank).
Also, the captain can't join the termies if they aren't in a transport (i.e. land raider of some sort).
First off I'd say you need at least one more rhino. I'd also say that this list is kinda inflated, you have 2500 points, but its not a good 2500 point list. It's an amalgam of what's in your armory. You'll have to pick and choose what will best create a coherent list.

I'd recommend dropping the list down to 1500 points. Keep the captain, and do the following (with your current list. This would require only buying one rhino):

HQ
Captain (145)

Elites
Dreadnought MM/HF (115)
Termie squad AC (230)
Sternguard squad 2 combi-meltas 2 combi-flamers (w/Razorback) (185)

Troops
Tac squad (10) ML/Flamer w/rhino (205)
Tac squad (10) MM/Melta-gun w/Rhino (210)

Fast attack
Land speeder MM/HF (70)
5 Assault (nilla) 100

HS
Dev squad w/4ML (150)
Pred (HB sponsoons) 90

That's a pretty powerful (not perfect) 1500 point list that incorporates alot of what you like, while not sacrificing too much competitiveness. It'll be fun, tactically flexible, and viable

I think the chappie is better than the captain in this list. If you run 10 assault tacs then it makes the unit work. No details of your load out on the unit in your list though.

Rather than a captain I would run a librarian in termie armour. He can either come out with the termies or remain in the raider for protection.

Standard LR is fine for tac termies, but if you want to run assault termies (and I maybe would) then I would put them in a redeemer.

4 ML Dev squad is fine, but the other squad less so. Plasma cannons are very expensive. I would probably run a second pred here instead.

MM Dread is close range - I would stick him in a drop pod with a DS MM/HF speeder for company rather than the assualt cannon version.

The real questions are more about how you will play. This is more important than your list. Anyone can write a list, its another question about how it will play!

Where will you stick your traitor?

How do you plan on grabbing objectives?

Why a chaplin over a librarian? How do you plan on making him really pull his worth??

How do you plan on using your vanilla terminators?

How do you plan on taking down heavy armor armies?

Will you be deep striking your squads?

What are your overall ideas of how to win each mission type?

What are your plans on how to deal with the armies out there? Go through each of the armies and make a basic plan on how to taclke them.
IG, SW, C:SM, CSM, Orks, 'Nids, GK, etc....

If I were you, I would drop the chaplain, drop the other devastator squad, give the termies an AC, and this combination to your tacs: flamer/meltagun.

To the remaining dev squad I would give either only Missile Launchers or Heavy Bolters, not both. As said earlier, another pred would also do good for your army.

You would be better dropping the rubbish Captain and taking Lysander to make those storm bolters on the Terminators twin-linked. Personally I would take a Chaplain in terminator armour and give the Terminators hammers and shield, re-roll to hit with them is evil.

The other problems is units in singles. You should take things in pairs, especially Land Raiders as one at this points level will be taken down to china town very quickly.