I don't think there is a single attitude toward death shown across the play as a whole. There are two key attitudes, really, I think: and they work against each other. One is that death is noble / the other that death is deeply unpleasant.
Here's Brutus, for example, talking about the murder of Caesar:
Let us be sacrificers, but not butchers, Caius.
We all stand up against the spirit of Caesar;
And in the spirit of men there is no blood:
O, that we then could come by Caesar's spirit,
And not dismember Caesar!
Death is a noble, unbrutal (note the pun on Brutus' own name) honorable thing. Except it isn't:
Of half that worth as those your swords, made rich
With the most noble blood of all this world.
I do beseech ye, if you bear me hard,
Now, whilst your purpled hands do reek and smoke,
Fulfil your pleasure.
That's Antony after the murder. It's not unbloody: it's horrific. And both Brutus and Cassius kill themselves in a supposedly honorable way: though, I guess, it's up to the production as to whether the deaths are as smooth as their moral justification. I saw one production in which the planned suicides were painfully botched and drawn out: in stark contrast to their easy morals.
As for your list of deaths: Caesar is murdered with knives by the conspirators. This is because they fear he is becoming too powerful, and needs to be stopped.
Cassius and Brutus both run on their swords, and commit suicide, both attempts at an honorable death, preferable to being beaten and enslaved after battle. Portia kills herself by swallowing fire - because she's mad. Titinius kills himself, after Cassius had died, with Cassius' sword in a gesture of honour toward his master.
Hope it helps!