Honda civic 97 stutters to turn on on first try?

I have a honda civic 97 which sometimes when i try to turn on it won't but the second time it does. And now the "oil light appeared" so it means that its been needing oil is that why sometimes it won't turn on because of lack of oil. And its also burning oil.

Sounds more like the fuel pump is taking longer to get gas to the engine

First, you've not provided 3 keys item in the car description: The trim level (Ex, Dx, Si etc) and A/T or M/T. Or the car has factory alarm system or not. It'll make a different in diagnose and wiring, switches in details.
Secondly, the terminology you've used is hard to understand even from talking with my customers on a daily basic about their vehicle cranking/ starting problem: Both are different:
'Stutter' or 'Turn on': What does it mean? Stutter as the starter trying to crank and quit then crank again or the engine trying to start but not or trying to run then stall out?
The normal daily terminology that my customers use would be: It won't crank, crank but won't start/run, the engine turn over but won't run, it start then stall out, it run then quit, it take a long time to start/run, the engine crank quit and crank again etc. You get the picture.
Now these are the things that you will need to check since I'm not clear what the problem really is with the cranking or starting: Provide the battery is in good state of charge or other mean: Good battery and battery cable terminals are clean and tight. The same with the starter cable/wire.
I'm using the wiring diagram for Manual transmission (M/T) instead of A/T (Automatic transmission).
1- See if you have a constant 9 volts or more at the starter solenoid BLK/WHT wire while the ignition switch is in "Start" position (III). If not: Check the starter cut relay plus the security starter cut relay (With alarm system). Both are good: Replace the ignition switch. See the diagram below.
2- Check the engine compression if the car has hard to start or has long cranking problem. What are the compression readings?
3- Is the engine smoking? What is the color? Blue or white? If it's blue: It's mean engine oil is burning inside the combustion chambers. The cause could be worn out valve guide seals and valve guides or the engine piston oil control ring has gone south. Oil burning is hard on the spark plugs and lead to hard starting problem beside blue smoke.
4- If the engine has no external oil leak then the low oil level is explain in #3. That explain while the 'Oil light' is on: Low oil level (Could be a defected oil pressure switch)
5- Same as #3 but white smoke: Either the injectors or the head gasket has failed. Is the car has overheat or loosing coolant? A fuel pressure leak-down test and a simple cooling system pressure test will confirm the problem. A fuel pressure test is also confirm the health of the fuel pump. What's the fuel pressure reading? Both fuel pressure and leak down tests can be perform at the same time.
6- Main relay: One of the two most notorious failed items when it come to starting/cranking or stalling problems on Honda in the same era: The ignition switch is another one. Read the link for testing and replacing either one: One the screen, look to the left column for the ignition switch http://techauto.awardspace.com/mainrelay…
A few things for you to start with to check on the car. The how to do the tests, if you're interest to know are available on youtube or you can send an E mail to me and I'll send the instruction and the needed tools/ pressure gauges to do the test. My E mail address is in my profile. HTH