i was fascinated by the idea of getting an impression of what the stage would look like from any seat, so i clicked on the interactive seating plan link.
however, as cute and as useful as it is, it actually just shows you the detail of the seating plan - not the view (which i THOUGHT was too much to ask!).
from my experience as a patron, and as an usherette in this theatre, about 15 years ago (but the seating appears to have changed very little):
cheap tickets are :-
the cheapest = standing room. this is behind the stalls circle and is FANTASTIC, especially if you know WHERE the BEST spots are to stand!
NEXT cheapest is UPPER slips - these are a TOTAL waste of time unless you are just there to HEAR the music (for example, at an opera performance). you CANNOT see the stage from MOST of these, as i recall...
NEXT cheapest is LOWER slips - the FEW seats closest to the centre of the theatre/furthest away from the stage, are BEARABLE - but only a FEW, literally 2 or 3. anything closer to the stage will have an EXTREMELY LIMITED view of the stage - you may only see one downstage corner! again, these seats are acceptable if you are there only to hear the music!
the NEXT price range is the BACK OF the amphitheatre - these are perfectly acceptable good seats, no matter where you are - although of course
the more central you are, the better. you can see EVERYTHING; it just looks a bit small! these seats are very high though, and therefore not suitable for the giddy!
next range is the LOWER amphitheatre and these are pretty much all very good seats indeed, with the proviso again that
the more central you are, the better. if you are way on the side, you will be missing the view of YOUR side of the stage, (especially the upstage corner). the FRONT row of the amphitheatre is FANTASTIC - but this would be getting a little bit pricey - comparatively speaking. the next couple of rows are also GREAT because all the amphitheatre seating is highly raked.
ADDITIONALLY, you might like to know that it USED TO BE that there were ONLY STAIRS to the WHOLE of this top level - no elevator. so you would not have wanted to have tickets up there, if you have any difficulty climbing stairs. HOWEVER - my guess is that this problem has probably been remedied, when the ROH was closed and renovated in the early 90's (but, with the british - maybe not!!!

)
my first choice when i was buying CHEAP tickets: standing room, then central back of the amphitheatre (even if that means the LAST row!), then the
end (only) of the LOWER slips (never the upper slips).
hope this helps.