Gatherer is great (sort of) for building decks, but I'd like the additional filter of specifying the search specifically to the cards I own. Is this a feature I'm just not seeing or is there an app of some sort that does this? I'd also like if it were always as up to date as Gatherer is.
To manage my collection, I have used deckbox.org. Since it uses gatherer as a "database" to know what all the cards are, it stays up to date with the current set. You will have to tell it what cards you do own however, so there is some up front work to tell the collection manager what you have.
It also uses magic.tcgplayer.com to let you know both the individual pricing of your cards and the contents of your entire collection.
As an additional resource, if you have an iOS or Android device, there is an app called Decked that I use for deck building. There are a lot of nice features to this app. Not only does the search criteria make it easy to find cards, it lets you create and manage decks right in the app. There are a lot of other useful features: it also allows you to test decks you've made in the app; you can have it automatically add the appropriate amount of land; you can see prices from multiple sources such as TCGPalyer and CardShark. Decked includes the ability to manage your collection so you can select cards and build decks exclusively using what you already own.
The downside to this is that, while there is a free lite version on iOS, the app does cost money if you want the ability to manage your collection: $3.99 on iPhone and Android, $5.99 on iPad, plus $2.99 for the collection manager (so between $7 and $9 total to get the management feature). But for the small cost, I find the benefits of this app are far beyond what I get with online search engines and collection trackers.
Mtgdb.Gui, a free program I wrote can do this.
The screenshot below demonstrates searching by text (left arrow) while limiting the search to the cards from collection you own (right arrow)
Besides managing your physical collection, you can import your collection and decks from Magic The Gathering Online, build your decks in Mtgdb.Gui and load them back into MTGO.
Wiki to get more information and screenshots
iMtG for iOS has full blown inventory management system linked with Deck Builder. It is completely free for people with collections which would fit in 3 binders.
iMtG is made by myself (as someone who cares), it has had regular database updates since 2011. It is important as many other MTG collection manager apps failed to keep updating their databases over the years.