The charm of Doris Day's innocent, girl next voice just grows over the years. This 1997 release on Columbia is the best value Doris Day compilation presently available, including lots of the earlier recordings, although I narrowly prefer the wonderful 1998 Columbia compilation
The Best of Doris Day [Columbia]. Just buy one, and relax into a simpler era.
If you want to start with a bigger collection: try the bargain 2008 2-CD set on Not Now Music,
The Best Of Doris Day [Not Now Music], which is actually the earlier 1-CD
The Best of Doris Day packaged with the CD reissue of the two Columbia albums
Day By Day/Day By Night from 1956/1957.
I've collated the recording years below. "Sentimental Journey" sounds to be the original version, released in 1945, rather than the 1964 re-recording. It became the unofficial anthem of soldiers returning home from the war and sold over 5 million copies.
1 Move over darling 1963
2 Secret love 1953
3 Whatever will be, will be (Que será, será) 1956 with Frank De Vol & His Orchestra
4 Lullaby of Broadway [78rpm version] 1951 with Harry James & His Orchestra
5 Love me or leave me [78rpm version] 1955
6 It's magic [78rpm version] 1948
7 Everybody loves a lover 1958 with Frank De Vol & His Orchestra
8 Dream a little dream of me 1957 with Paul Weston & His Music From Hollywood
9 Pillow talk 1959
10 Cheek to cheek 1958 with Frank De Vol & His Orchestra
11 Fly me to the moon (In other words) 1964
12 Close your eyes 1961 with the André Previn Trio
13 Quiet nights of quiet stars (Corcovado) 1964
14 Night and day 1958 with Frank De Vol & His Orchestra
15 Let's face the music and dance 1958 with Frank De Vol & His Orchestra
16 Pennies from heaven 1958 with Frank De Vol & His Orchestra
17 Over the rainbow 1958 with Frank De Vol & His Orchestra
18 I'll never stop loving you [78rpm version] 1955
19 If I give my heart to you [78rpm version] 1954 with The Mellomen/Frank and Frank De Vol & His Orchestra
20 Bewitched [78rpm version] 1949 with The Mellomen
21 A very precious love 1957 with Frank De Vol & His Orchestra
22 The Black Hills of Dakota 1953 with Paul Weston & His Orchestra
23 Teacher's pet [78rpm version] 1957 with Frank De Vol & His Orchestra
24 Makin' whoopee 1959 with Frank De Vol & His Orchestra
25 Ready, willing and able [78rpm version] 1954 with Buddy Cole & His Orchestra
26 Sentimental journey [78rpm version] 1944/5
Update 2012: check out the 3 CD, 60 track compilation
Day By Day - The Greatest Hits & More. Regrettably "Bewitched" is missing and it omits "Move over darling" (not a problem for me), but it's a very strong offering.