If you have access to Xanathar's Guide to Everything, it offers the Eldritch Invocation 'Improved Pact Weapon':

You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.
In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.
Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

That first line partly solves your problem - it makes your weapon your focus, which allows you to cast spells with a material component while holding a weapon and shield. (The rest of the invocation is just gravy.) From there, if you take War Caster you can cast all spells, or if you don't you can cast any that don't have a somatic component while lacking a material component.

If you have access to Xanathar's Guide to Everything, it offers the Eldritch Invocation 'Improved Pact Weapon':

You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.
In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.
Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

That first line partly solves your problem - it makes your weapon your focus, which allows you to cast spells with a material component while holding a weapon and shield. (The rest of the invocation doesn't impact on this particular question.) From there, if you take War Caster you can cast all spells, or if you don't you can cast any that don't have a somatic component while lacking a material component.

If you have access to Xanathar's Guide to Everything, you don't actually need the War Caster feat for this at all. XGtE offers the Eldritch Invocation 'Improved Pact Weapon':

You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.
In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.
Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

That first line solves your problem - it makes your weapon your focus, which allows you to cast spells while holding a weapon and shield. The rest is just gravy.

If you have access to Xanathar's Guide to Everything, it offers the Eldritch Invocation 'Improved Pact Weapon':

You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.
In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.
Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

That first line partly solves your problem - it makes your weapon your focus, which allows you to cast spells with a material component while holding a weapon and shield. (The rest of the invocation is just gravy.) From there, if you take War Caster you can cast all spells, or if you don't you can cast any that don't have a somatic component while lacking a material component.