ばいいCan, Should, It'd be good if

Both たほうがいい and ばいい are used to give suggestions. たほうがいい is a straightforward 'You should…', while ばいい adds a nuance of 'All you have to do is...' or 'Why don't you just...?' Depending on context, ばいい can sound more friendly, but it can also sound a bit pushy. Unlike たほうがいい, ばいい is commonly to be paired with のに to express 'It would be good if (A), but (A) isn't possible).'

ないほうがいい is used to advise against doing something, similar to 'You shouldn't…'. It's a common expression that reflects the speaker's personal or subjective opinion. In contrast, ばいい suggests doing something, with a nuance like 'All you have to do is...' or 'Why don't you just...?' Unlike ないほうがいい, ばいい is often paired with のに to express 'It would be good if (A), but (A) isn't possible).'

When followed by いい, both ば and と express 'if you do (A), it would be good', but with different nuances. ば conveys uncertainty and is used for unlikely events, e.g. 'It would be nice if (A)', implying that it probably won't happen. と is stronger, often implying hope, e.g. 'I hope (A) happens.' Depending on context, といい can also suggest 'You should (A).'.

はずだ indicates something is expected based on information or logic, as in 行けるはずだ ('I should be able to go.'). ばいい expresses hope or a hypothetical good outcome, like 行ければいい ('It'd be nice if I could go.'). One is based on reasoning, the other on desire.