Choose the best word (or words) that should fill the gap:
We have to be careful with our remaining money, so let's choose the ... ... menu.
If you chose Answer 1, dare we suggest that either you are very rich, or you weren't thinking straight?
Answer 2 is right; Answer 3 would be understood, but isn't quite 'proper English'.
'Cheapest' is not factually wrong, but like many words connected with the big issues in life (money, birth, death, health, sex, home, work etc.) it has 'overtones' ... in other words, it suggests all sorts of other ideas without actually saying them. 'Cheap' is a perfectly good and serviceable word, but we can be sure that most of you would know what we mean by 'a cheap hotel', and even if your money is short, you would prefer not to stay anywhere quite like that.
Sometimes we talk about things being 'cheap and cheerful' (i.e. they don't cost much, they're probably not very well-made or prepared, but they are OK for a short-term purpose, and we can be glad to have them for the time being).
If you watch British television soap-operas ~ to improve your understanding, and maybe pick up some 'cultural' points ~ you may hear one character criticise another for making 'a cheap remark' (= a cruel or tasteless word, easily said, and hurtful to another person), perhaps that they called a woman 'cheap' (which we will not go so far as to explain here; think it through, or look it up elsewhere, if you really feel you need to).
On a lighter note, one of the oldest English puns ( = wordplay, where two words with different meanings sound and/or look the same) is about a pet-shop where they offer 'Baby parrots going cheap' (i.e. you can buy one for only a little money if you want it; but 'cheep' is our English word for the high-pitched sound that tiny birds make when they first open their beaks. Like all good noise-words, it even sounds rather like what it means, where 'the little chicks go "cheep, cheep, cheep"!)
... Not to be confused with Tweets and Tweeting, which (until fairly recently) meant more or less the same thing ...