You don't need to use CHOOSECOLS as the formula is already filtering the entire table, therefore, the entire table (all columns) will be returned in the result. If you were filtering a larger table (more columns) and wanted to return a select few, then CHOOSECOLS would be needed.

As for the filter, if you wanted to use F2 for either the partial name OR the partial IP the you would need to use the + symbol to join the two criteria within the FILTER function.

=FILTER(Table1,
  (ISNUMBER(SEARCH($F$2,Table1[Client_Name])))+
  (ISNUMBER(SEARCH($F$2,Table1[IP_Address])))
)