BrokeFarmerJohn - I am heavily involved in the administration of a Township in the Dayton area so my questions/comments are from that perspective. My township surrounds a small city (population approx 5500). But, my comments/questions are my own and not any official representation of the Township....
You show that you're in Columbus. Would you be annexed into Columbus or one of the suburb cities?
How much land do you have? If you are on a typical "city size" lot (1/4 - 1 acre), being annexed might not make that much difference for you, other than the additional income tax. But if you have more of a "Township size" property (2+ acres) and are used to doing what you want to do, I'd fight the annexation. Depending on your "activities", you're going to have a lot more red tape (and just more crap in general) dealing with the city zoning office rather than the township zoning person. If you ever discharge firearms on your property, you're most likely no longer going to be able to do that if you end up within the city. Just something simple like building a shed will have double the paperwork and at least double the cost for permits, etc. Depending on the city, they may have an over zealous city inspector that likes to put "Violator" signs in your yard if your grass gets a little too long in their opinion. (The little city I moved from had one of those! Ugh!)
Look on the city's website for their local regulations to see about your animals. As someone mentioned, get any promises regarding keeping them in writing. You may be able to keep the ones you have, but might not be able to replace them.
Check with the county regarding your septic. You might not be able to just hook back up to it. I think the law in Ohio is that any new septic has to be a "mound system" which generally runs somewhere in the $10-15k range, from what I've heard. You might be able to "replace / repair" the existing septic with a traditional tank and leach field. I know my neighbor across the road (different township from me, however - but I think the county laws prevail with regards to septic) just replaced/repaired their septic with what looked like a traditional install.
I'm assuming that you work in a township or other non-taxing district if you're going to have to start paying city income tax if you're annexed. If you are already paying city income tax to where you work, check with the resident city to see if they have a "Resident Tax Credit" available to offset the combined amount of resident and non-resident city income taxes. If any of this applies to you, post it up (or PM me) and I'll try to give you some more information on this.
Back to the firearms issue... The city that we surround annexed several farms many years ago. One small farm (14 acres) was for sale a few years ago and I was surprised to find that it was within the city limits. I looked at the local ordinances and found that discharging firearms within the city limits was prohibited. I called the city and asked if there was any sort of "rural exemption". I was told absolutely not. I said "what if a coyote is in my chicken coop?" Was told to call the cops and wait for them to do something about the coyote. Decided to stay put!!
If your city posts the minutes of their council meetings on the website, do yourself a favor and download AND READ the minutes of the meetings for the last year or so. It will be dry and boring, but it will also tell you the attitudes of city council and how they do things. I know that I want no part of the city that our township surrounds based on what Council does!
As an accountant, I think that the advice that you've already been given to get the costs for drilling a well and addressing your septic issue is good. If there's a reasonable payback, I'd lean towards staying in the Township. Even if you have to rely on the County Sheriff's office for police protection, if you have a real emergency, ask the dispatcher to "request assistance" from the city if the sheriff is going to be a while to respond. Our local departments assist each other all the time. Our Township has its own Police Department, but there is generally only one officer on road patrol at any given time. If the other side of the road from you is the city, then the city has jurisdiction on the road itself and will (or should) assist for calls on the Township side of the road.
Double check your property taxes. Your county auditor should have a site where you can type in your address and see all of the levies that apply to you. For example, in our township, we pay our Township Police Levy, but if the city annexed me, I wouldn't pay that any more. BUT, the city might have their own police levy that might be more. You want to check the levies in place for your property (and note the millage of the levies) and then check the same information for an address for a city property that is close to you. Compare the total millage to see if your overall property taxes will go up or down if you are annexed into the city.
You might want to consider finding out when the next Township Trustee meeting is. Generally Trustees only meet once or twice a month so find out quick. I'd hate to see you have to wait another month to talk to them. But, go to the meeting and find out if they've dealt with this before and can they give you any help or advice in dealing with it. Hopefully they will be helpful. But, call to find out when the meeting is and ask if you can be on the agenda. Otherwise the Trustees might have a "visitor comments policy" that limits you to 3 or 5 minutes and they don't (legally) have to interact with you. If you're on the agenda, it gives them a heads up. Generally, smaller township's meetings are pretty relaxed though.
If it's inevitable that you're going to end up in the city, I might think about spending a few bucks with an attorney to see if you can get out of paying for any of the associated costs. Basically the costs are going to be related to all of the filings that go on with the county auditor to move you from one taxing district (Township) into another taxing district (city). There is also a pretty substantial cost for the County Engineer to reprint the local, official maps showing municipal boundaries, zoning, etc. If the city wants you to be in the city to start paying income taxes, see about having them eat some of those costs.
Good luck with this.