I'd say your difficult-to-remember song is most likely:
Kiss Me, released in 1997 by Sixpence None the Richer (Listen on YouTube)
Based primarily on:
(i) the first letters of each line spelling 'SNOG' (a synonym for 'kiss') in reverse;
(ii) the final line referring to the band's name.
Words similar to the partial lyrics listed are found in the following songs also released in the 1990's:
Gardens, new cars, and a house up in the hills.
I Will Buy You a New Life, by Everclear (1997):
I will buy you a garden
Where your flowers can bloom
I will buy you a new car
Perfect shiny and new
I will buy you that big house
Way up in the West Hills
Oh May, do you want to get married, or run away?
Slide, by Goo Goo Dolls (1998):
Put your arms around me
What you feel is what you are
And what you are is beautiful
Do you wanna get married?
Or run away?
Now I'll get over you, I know my ship's not sinking.
King of Wishful Thinking, by Go West (1990):
I'll get over you I know I will
I'll pretend my ship's not sinking
Potentially of note is that:
The titles of these songs begin with the letters of 'KISS' (albeit with only one 'S'), which may be another nod towards this particular song.
(Alternatively - and yes, this is a joke - there may be a further acrostic at play here using the band names; in which case, to quote a movie from 1993 (the same era as this puzzle): I'm not kissing no EGG.)