DISK I/O

What you're describing is exactly what the Toolbox function PBCatSearch does. It's extremely powerful and versatile, which unfortunately implies that it takes a little work to set it up right. You could just about write a clone of "Find File" in FB, using practically nothing but PBCatSearch. (In fact, I'd bet 5 bucks that "Find File" is essentially just a front end for PBCatSearch.)

Below is a demo: it finds up to 25 files whose names contain a given input string. This is just one of many different ways that PBCatSearch can search.
To get the full scoop on PBCatSearch, check out the following links:

http://developer.apple.com/techpubs/mac/Files/Files-94.html

http://developer.apple.com/techpubs/mac/Files/Files-252.html

'================
' PBCatSearch Demo, by Rick Brown
'======== constants ==========
_maxRequest = 25				'Adjust as desired
_searchInfoSize = 104
'========= globals =========
DIM RECORD fsRec
  DIM fsVrefNum%
  DIM fsParID&
  DIM 63 fsFilename$
DIM END RECORD _fsRecSize

DIM RECORD catPositionRec
  DIM initialize&
  DIM priv.12
DIM END RECORD _catPositionRec
END GLOBALS
'========= functions ============
LOCAL FN PBCatSearchSync(cspBlockAddr&)
  `	 MOVE.L  ^cspBlockAddr&,A0
  `	 MOVEQ   #$18,D0
  `	 DC.W	$A260
  `	 MOVE.W  D0,^OSErr
END FN = OSErr
'========= MAIN =============
DIM cspBlock.76, searchInfo1.searchInfoSize, searchInfo2.searchInfoSize
DIM fsSpecArray.fsRecSize(_maxRequest)

WINDOW OFF
WINDOW 1
TEXT _monaco, 9
INPUT "File name to search for: "; searchFile$
IF LEN(searchFile$) = 0 THEN END

'(use the following values as an example)
volumeID = -1					'(use startup volume)

cspBlock.ioCompletion& = _nil		    	'(no completion routine)
cspBlock.ioNamePtr& = _nil			'(don't use volume name)
cspBlock.ioVRefNum% = volumeID
cspBlock.ioMatchPtr& = @fsSpecArray(0)
cspBlock.ioReqMatchCount& = _maxRequest
cspBlock.ioSearchBits& = _fsSBPartialName%	'(only care about name)
cspBlock.ioSearchInfo1& = @searchInfo1
cspBlock.ioSearchInfo2& = @searchInfo2
cspBlock.ioSearchTime& = 0			'(no time limit)
cspBlock.ioCatPosition.initialize& = 0		'(start at beginning)
cspBlock.ioOptBuffer& = _nil

'Set values to search for:
searchInfo1.ioNamePtr& = @searchFile$
searchInfo2.ioNamePtr& = _nil

PRINT "Searching..."
OSErr = FN PBCatSearchSync(@cspBlock)
CLS
SELECT CASE OSErr
  CASE _eofErr, _noErr
	count = cspBlock.ioActMatchCount&
	PRINT "Number found:"; count
	LONG IF count > 0
	  INPUT "Press RETURN to list them:"; x$
	  FOR i = 1 TO count
		PRINT fsSpecArray.fsFilename$(i-1)
	  NEXT
	END IF
  CASE ELSE
	PRINT "OSErr = "; OSErr
END SELECT
PRINT
INPUT "Press RETURN to end:" ; x$
'===============