POSIX shells use space as field separator. Variable names must match the regex [a-zA-Z_][a-zA-Z0-9_]* (i.e., must start with a letter or underscore, followed by zero or more letters/digits/underscores). (So wacky variable names such as _ or _1 are technically permissible--if ill-advised.)
$foo is shorthand for ${foo} and the two are interchangeable most of the time. If the variable is followed by a character that is allowed to be part of a variable name, then you need ${foo} to prevent ambiguity. You can never go wrong with ${foo} but it's not needed here--shell does not allow a period to be part of variable name, so there is no ambiguity in $foo.extension
${foo}.bar and "${foo}.bar" are interchangeable unless the value of ${foo} contains a space, in which case the shell would get confused and interpret the value of ${foo}.bar as two separate things (delimited by the space inside the variable foo).
Bottomline:
From the code snipped we know that DB does not contain a space, so quotes are not required. What follows the variable name (a period) cannot be confused for being part of the variable name, so curly brackets are also not required. So all three forms you listed are fine. I've seen forms #1 and #2 in TCL scripts. Personally I'd go with #2 because it avoids me having to type the unnecessary curly brackets (vs. #3) and it would still work if the value of DB were to change in the future to include a space (vs. #1).
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