If your old AKG is a dynamic mic (since you compare it to an
SM58) then you don't need to go to $400 for an audible difference. ANY condenser is going to have a very different character. However, if your budget is up to $400 then you can jump the "cheap LDC" phase most of us go through and get into some rather good mics.
Ones to put on your short list:
sE2200A II
Rode NT2A
Rode NTK (if you can stretch your budget or find a bargain--lovely mic for the vocals you describe)
AKG C214
To give equal time, also look at large dynamics like the EV RE20 and Shure SM7B. Their sound isn't my cup of tea but many on this forum like their warm, less crisp sound.
I'm not dissing the Oktavas that have been recommended--just never heard them in any sort of controlled environment.
My personal choice from the above list is the sE2200A. I have several and they've become my go to mic for vocals, especially female vocals, even over some rather more expensive Neumann mics I have in the cupboard.
If your shop lets you audition mics, that would be ideal as every voice is different and everyone's idea of what sounds good is different.
Last point: assuming I'm right that your existing mic is a small dynamic, there's a good chance that it'd still be the best bet for miking a guitar amp.