Theres two general lines of thinking who you send in your first troops;

1,Send in troops who are expendable and of lesser quality than those you wish to protect. The good side is that even if casualties are significant the troops you lose you don't really care about, the bad side is they could be utterly routed and you lose a portion of your army. Compromising your chances of victory.

OR

2, Send in your best, the men you trust the most, the good side is being your finest they are more likely to succeed, the bad is that you never want to lose troops you care about alot of money to recruit and train. You could possibly lose your best men in a failed assault or simply incur heavy casualties resulting in poor effectiveness in later battles.

Its a fine line you have to walk, I tend in sieges were the danger of defeat I estimate at say 20-30% to send in mercenaries, but most of all expendable troops like auxillaries and troops native to foreign lands. If the stakes are higher I send in mercenaries backed up by some more important troops 1 or 2 units of principes for example.

If the stakes are really high and the city simply must be taken, then I send in the bravest and best, the finest men I have.

Overall the best general strategy is to use both to support one another, never leaving it to chance that your weaker troops could be slaughtered by having better troops nearby.