After the 'Cold War Dividend' layoffs in the Army I used my GI Bill to get a California POST Certificate to increase my chances of being hired as a lateral as opposed to as an untrained starting recruit position. It was interesting, I learned a lot, I had some fun times too, BUT it didn't help.
Competition was fierce for few openings and I had a misspent youth (lol) that didn't help at all. I spent 3 years working construction jobs and testing everywhere there was an opening. To maximize your ability to be tested you'll need a flexible work schedule. Getting to know a few LEOs and buying into a jobs listing magazine helps in knowing where jobs are. Not all job openings are highly advertised. I got to final Chiefs interviews many times but never got a break. Then I applied to the USBP. That was a good move as they were on a huge recruiting drive at the time. Go where the jobs are!
As others have said don't limit yourself to just local and state agencies. Do federal applications as well (OPM lists them at USAjobs.gov). Get your foot in the door somewhere. Be willing to relocate. Get fit and stay fit. Being tops on the physical fitness tests they run impresses prospective employers greatly. Be frank and candid about your past They'll find out anyway if your concealing something. Keep at it, it takes time and work. If I could get hired you should be able to as well unless you are hiding some undisclosed past.
I had a felony arrest on my record with no conviction, but my youthful behavioral issues were mitigated by a good 10 year army record (Letters of reference from field grade former military bosses) and candid honesty in interviews and background checks.
I don't think anyone knows if they will like their job in Law Enforcement until they arrive at their job. There is a ton of variety based on where and by whom you get hired. As far as being the new guy rookie etc - that happens in all jobs, it's just a bit more pronounced in some professions. For me I was happy for 4 years then I hit a wall and went back to the Army. Such is life.
Good luck to you! Cheers!
One last thought. Keep a copy of your first background investigation forms, you'll be filling in that info over and over and over. It will save you much heartache. If you've had a Federal security clearance in the past get a copy of that investigation form too from your current or former security manager. Agencies cross reference all those forms and if there is any discrepancy you will be in trouble.
Edited to add: Don't do one application at a time, do as many as you can possibly do concurrently. The applicants to jobs rate in my experience was abysmal. Hundreds to thousands to one. The recruiters will cull applicants heavily initially to pare down their applicant pool to a manageable size. Expect a lot of rejection letters and don't let that get you down.
Oh-ya, and to state the obvious -> get a short conservative haircut, be clean shaven, have an appropriate suit and tie and polish those shoes! My observations while job hunting was that those that didn't fit that model usually got culled fast from the vetting process. Be serious. If you get left in a room waiting hours for some process or another etc behave yourself. Eyes will be on you even when you may be unaware of it.
Expect hypothetical problems to be thrown at you in interviews. Think before answering them. Don't waffle on your solutions. Don't be an idiot. If you are not an Alpha personality do your best to get in that frame of mind.
If you get a rejection letter find out why so you can improve on your next application. Ask the recruiter if they know any other agencies that are hiring, especially if you've progressed a long way through vetting. Often times if they think you were a strong candidate but not the best for that cull they will refer you to other agencies. That happened to me many times.
For Federal applications: OPM uses forms and tests to make a list of best to worst applicants. Be well rested and arrive early to the federal building. Expect it to be a long boring slog of a day. Before starting they will lock the doors on those who are late. After testing expect an interview by your hiring agency. Once OPM establishes a list the hiring agency must work down that list in hires. Sometimes they have just one list but they can have many. I've known many agents who didn't get a job offer for years after applying. My job offering to the USBP came in a registered letter and I had a 24 hour window to accept or decline, I then had 3 days time to report to my sector headquarters in South Texas from my home in California. Be prepared to move fast if they offer you a job. If you do get hired do not take any weapons to FLETC. In my USBP class 2 trainees from a class of 40 were fired and arrested on the spot day one for being idiots that couldn't follow instructions, rules, and laws.