I'm making a big assumption you are doing American style, because country music is more popular here. I go to a lot of places where only country music is played, and even though I do the country dances, I am constantly looking for a song I can do ballroom to because that is my favorite. For practice purposes, a country song can work, much as it does for me at a country place (even though I can think of better choices). For the dances you listed, here are some that will work:
Foxtrot:
From a Jack to a King by Ricky Van Shelton
Goodnight Sweetheart Goodnight by The Statler Brothers
I'll Take Texas by Vince Gill & Shelby Lynne
All Of Me (Loves All Of You) by George Strait
Eat At Joe's by Suzy Bogguss (also works as a West Coast Swing)
Side By Side by Kay Starr
I'm Moving Along by Pasty Cline
Waltz Me Once Again by KD Lang
Blue by Leann Rhimes
Waltz
I'll not list these. There are many. Just look for some 3/4 time music that's not too fast.
Rumba
There are a lot of songs that will pass for a rumba. The country music dancers use many of these for cha cha, but in my opinion they aren't very good cha chas and work better as a rumba. Most country bands have a lot of trouble imitating Latin music.
I Just Want To Dance With You by George Strait
I Can See Clearly Now by Anne Murray
Neon Moon by Brooks & Dunn
One Night At A Time by George Strait
Dancin', Shaggin' On The Boulevard by Alabama
Gulf Of Mexico by Clint Black
Two Pina Coladas by Garth Brooks
My Maria by Garth Brooks
South Of Santa Fe by Brooks & Dunn
Other songs, not necessarily country songs, but done often by country bands that are also rumbas are: Spanish Eyes, Under The Boardwalk, Up On The Roof, Slow Hand, Blue Bayou, and Spanish Harlem.
Samba
I know on NO country song that has a samba beat.