In act 1, scene 1 of Othello, what are Roderigo's and Iago's feelings toward Othello?

Othello is the tragic story of how miscommunication changes lives. The audience is introduced to Othello through the words of Iago and Roderigo in Act I, scene i with Othello only making his entrance in scene ii. It is possible, and apparently purposeful on Shakespeare's part, that if Iago is to be believed, Othello is  a person who "loving his own pride and purposes" (12) has made an inappropriate choice for his lieutenant, and unfairly passed over the most-deserving candidate (who is of course Iago) from "whom his eyes had seen the proof" (28). The audience is even possibly inclined to feel the same way as Iago, and this is encouraged by Roderigo's part as he too feels that Iago is justified to "hold him (Othello) in thy hate" (7). Roderigo is so enraged by Othello's apparent poor choices and is already falling into Iago's trap. He too would despise Othello if his reward for success in battle was to be nothing more than to be Othello's "ancient" (33). 

Iago admits that he will take the first opportunity "to serve my turn upon him" (42). Iago also knows that Roderigo has his own reasons for disliking Othello and that Roderigo relishes any chance to get closer to Desdemona. He acts and speaks before he thinks and Iago intends to make use of this characteristic to further his own aims. Roderigo knows that Brabantio (Desdemona's father) has turned him away before, for being unsuitable for Desdemona, but he is so inspired by Iago's talk of revenge against Othello, that he demeans himself, "a knave of common hire" (126) so that he can reveal Othello as even worse- "a lascivious Moor" (127) and so help Iago destroy Othello's reputation and standing, such is the level of his self-absorption. He does not realize that his words do not make him a better candidate for Desdemona's attentions. It becomes obvious, therefore that both men despise Othello for their circumstances rather than looking at their own shortcomings. 

In Othello, what are Roderigo's and Iago's feelings towards Othello?

Iago and Roderigo both despise Othello but it is Iago who has an irrational desire to ruin Othello. Roderigo's hatred is based on Roderigo's own apparent 'love' for Desdemona. He is so foolish that he thinks that Desdemona can be his if only Othello is out of the picture.

Roderigo is Iago's pawn, doing his bidding and even paying Iago to secure his favor with Desdemona. He allows Iago to manipulate him and even when he realizes that Iago has only his own interests at heart, "I do not find that thou deal'st justly with me"  and he has "wasted myself out of my means"  he is still persuaded to act to secure his love interest.

The hatred Iago has for Othello is immeasurable and, in some instances, unfounded. He is paranoid and believes Othello may have even

  leap'd into my seat; the thought whereof
Doth (like a poisonous mineral) gnaw my inwards

He has no reason to think this and even Emilia tells him it's absurd.

The fact that Cassio was promoted sets Iago off on his path to destroy Othello as he cannot believe that there is any sensible reason why Cassio would have been promoted over him, an experienced soldier.

Revenge is the main motivator for Iago and all his actions come together so that it appears that he is not the only instigator, having most of his compatriots believing he is "honest" Iago.

It is perhaps the similarities between Iago and Othello that push Iago to destroy Othello and all those connected to him

Iago is the only character who speaks directly to Othello's sense of his own inadequacy.

Iago almost relishes his devilment, "I am a very villain else" and his feelings towards Othello do not falter. Each occurrence serves to strengthen his resolve and with Roderigo as his willing co-conspiritor, he cannot be stopped.