"Is it ok to use the chemicals once just to get some control of the situation and then switch to organic care? I just want to do the right thing. "

I think that's a personal choice. I use a mostly organic approach, but will occasionally spot spray. Some people take a hybrid approach and use one application of synthetic fertilizer in late fall. Others won't use anything that isn't organic.

In Indiana, your grass is probably mostly KBG, so if you water deeply and infrequently and mulch mow at the highest setting, the KBG will thrive and spread and over time, the weeds should diminish. But if you want quick results, you'll almost have to use some form of chemical weed killer.

The best way to get rid of those "weeds" is to grow a good, healthy turf and that means startin gwith a good, reliable soil test. Start by contacting you county office of the Purdue USDA Cooperative Extension Service about having that soil test done, then dig in with these simple soil tests,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer you soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
that can help guide you to that good, healthy soil.
Mow your lawn high, as high as the mower will allow since that will expose more grass blades to the sun so those grass blades will be able to manufacture more nutrients to feed the roots so the roots can grow more grass plants which will help crowd out those "weeds".
Inlike many people I do not get all kinds of paranoid about some "weeds" in my lawn. The presence of "weeds" is after all normal while the absence of "weeds" is unnatural, artificial.

Here is a link that might be useful: Purdue CES