How can I select particular elements by an increasing step in rows?

This is easy using linear indexing (a loop is not required):

>> [M(1:10:end);M(2:11:end);M(3:12:end);M(4:13:end)]
ans =
   10   20   30
   11   22   33
   12   24   36
   13   26   39

Note that M has 10 rows, so you can easily adjust the code I gave to work for any number of rows:

>> S = size(M,1);
>> [M(1:S+0:end);M(2:S+1:end);M(3:S+2:end);M(4:S+3:end)]
ans =
   10   20   30
   11   22   33
   12   24   36
   13   26   39

Note that this method only works if the number of columns is <= the number of rows.

To adjust for N elements from each column you can add a loop, either following the method above:

N = 4;
Y = nan(N,size(M,2));
S = size(M,1);
for k = 1:N
    Y(k,:) = M(k:S+k-1:end);
end

or doing a naive implementation of what you explained in your question.