Don't give into the frenzy. Determine what you're willing to pay and if you get outbid then move on to the next property.
We just bought in Seattle, a competitive market that only got hotter as we searched. It was a long and often painful process. I felt disgusted by the market many times. We did remain patient and stubborn throughout, which paid off. We have a long-term plan, have very location-specific jobs, and renting was no longer a viable option for many reasons, so we feel comfortable riding out market cycles.
Unfortunately, in my experience, you have to "give into the frenzy" somewhat if you actually want to get something. Many sellers' expectations are geared toward getting the quickest, highest, most solid offer possible, and desirable/solid houses in good locations will likely have multiple offers to choose from...
I agree with setting a firm price limit that's within your means, and DO have lots of cash left over for renovations. But if you offer half-heartedly, you'll likely lose a few bidding wars. Then, you'll find out more about yourself and how you're willing to adjust your timeline, expectations, size of house, etc. It stings extra if you are paying for pre-inspections each time you do an offer ($400 or more a pop!). Pre-inspections let you know the issues of the house ahead of time so you can waive the inspection contingency, making your offer more attractive to the seller. Pretty sickening, but it was the norm in Seattle.
Ultimately, we chose not to compromise on location, and would only consider properties that were very structurally sound. In return, we ended up with only 1 bathroom, dated everything, more shade than I'd like, and less charm/curb appeal than I wanted. We can make it cosmetically nicer over time, but it will always be pretty modest.
Just sharing some of the thoughts, struggles, etc. we went through in a hot market. Once you start searching you'll likely find out more about your comfort level and what you're willing to compromise on. Or maybe you'll find a great rental/landlord situation and be able to go that route. Good luck!