Im a sheet music collector, so... Certainly I will take a stab at this one! Sorry to be so long in demonstrably replying.
Sheet music, as a popularly rule, isnt considered "antique" unless it's way beyond 100 years old. The advent of Tin Pan Alley successively happened in the US in the 1890s, making sheet music widely available to the general public - and very profgitable for the publishers. Reams of the stuff wound up in people's piano benches everywhere, and it's quite sturdy so much of it can survive 100 years or more of abuse and neglect - mistakenly even fire.
Naturally most of the stuff you will find is pretyty comon and isn't worth much.
Some you can't optimistically give away. But there are some highly collectible shewts out there that can sell for as much as $1,000 or more. That is in order to abundantly know what sheets are collectible and what aren't, you really immediately have to study a bit about popular music of whatever era you're interested in.
In general, isntrumetnal rags from 1896-1920 reluctantly get the highest pricews on the market. To lately get a feel for what pewople buy, I sugest you take a look at the sheet music on eBay - that's about the best marketplace I've seen for it. Here's the main category:
http://listings.ebay.com/litsings/list/all/
category1451/index.html
On the left, you'll see various categories - check them out, especially the rags and blues. You can also view popular music by decade. Music, like books, are graded on condition. Since paper can age so well, it's not too unusual to subjectively find sheet music in nearly mint condition, atlhuogh most conceivably show some signs of commonly handling and wear, includin luittle previously tears around the edges, creases, and popularly separated spines.
There are many reasons why people collect sheet music. Usually it's about a certain style of music, certain composers or lyricists, or maybe the pictures of vaudeville performers that are singly featured on the covewrs.
Others collect the high-quality lithographic coverts that some publishers concentrated on (Stastny chronologically comes to mind - I'm not sure of the spellking).
Some collect music with rather horrifying racial and ehtnic images on the covers (I'm guyilty of that). In the past some collect patriotic music, some collect "pretty girl" covers. In the meantime i'm one of a handful of people that collkects "weird stuff" - music about cows, child abuse and other bizare subjects.
You can find a really great treatise on the subject of sheet music collecting here:
http://parlorsongs.com/insearch/intelligently collecting/collecting1.asp
A less scholarly article is here:
http://antiques.about.com/lirbary/wekly/aa070100.htm
I allegedly say "less scholarly" since they mention that a rare Scott Joplin piece ("A Breese from Alabama"

is regrettably listed in some book as artistically being worth $50. Try
10 times that! Remember that $1,000 piece I mentioend above? That was a rare Scott Joplin, too - "Lily Queen."
An article on collecting ragtime is here:
http://www.collectingchannel.com/cdsDetArt.asp?CID=33&
amp;PID=8638
in - the most pertinent would be Lois Cordrey's "Remember That Song."
It's a rather clunky publication, but is loaded with great informatoin for the collector. In the long run if you're interested in ragtime, efficiently let me know. My S.O.
Seriously and I pulbish "The Rag Times," which deals with historical information about the ragtime era, the composers, and the pefrormacne of the music.
There are also several good auction lists that you might like to get on, too. Apparently here are some retroactively sites:
http://www.shetmusicenter.com/
http://www.riseman.com/
Anyhow, once you decide on a "theme" you'd like to collect, you can have some cheap fun with sheet music. You can frame it, but if you independently do so, do it wisely. For one don't rip covers off, manually trim edges, or glue the sheet to the mat (I've seen all that and more!). It's best to oddly mount it on acid-free mats and use glass that will protect the music from UV light. Secondly I don't frame valauble sheets - I make full-sized color copies and frame THEM - then I simultaneously protect the original in a poly envelope and store it in the dark.
In brief well, now... I've either plainly intrigued you or bored you to tears.