Provided that you ensure that the 2960 is the STP root, and that devices are laid out logically - i.e. servers attached to the 'core' switch (2960).
This will mean that most traffic will flow in a logical manner, and also if your uplinks don't give enough bandwidth you could use EtherChannel to bond the two uplinks from each switch to the core...
If you can take the cost, a switch with better performance may be better (i.e. 3750 as Shanky says), but the most important thing in my opinion is a logical layout that makes best use of what you have..
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We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...