Unless you severely misconfigure your firewall, it can only help. The overhead of firewalls is usually pretty negligible unless you have a really complicated ruleset. Remember, all it is doing is checking incoming packets against a set of rules. Also remember that firewall setups are a given in even the smallest enterprise environments with public facing servers. Even a small home router or desktop can really only benefit from having a firewall. Think of your login password. The chances of someone breaking into your house and using your computer are slim, but the "overhead" of password protecting your account is so negligible that you might as well just do it. You've provided no information as to your setup other than that you are running a web server with a public IP. I can't tailor my answer to your setup.
It is likely you have a few other ports open on that machine, (ie. SSH or some NetBIOS or RPC stuff if it is Windows). A firewall would allow you to leave port 80 open for general business while preventing possible exploits of other services you have running on your box, knowingly or unknowingly.
Additionally, some most firewall packages like PF and Iptables can be used to thwart scanning and abuse of your legitimate public facing servers. For example, if you have a service being brute forced by a bot, you can block that IP with your firewall while allowing other IPs to continue accessing your webserver. Most firewalls have built-ins or addons to automate this process (ie. fail2ban and sshguard).
A properly configured firewall should not make you more susceptible to a DoS attack. It would help prevent against a SYN flood because you can block offending IPs. Of course, source IPs can be forged to random values to avoid this. However, PF uses "synproxy" which can mitigate this. A Teardrop attack could be prevented by a firewall as well (ie. the "scrub" anchor).
In summary, there are plenty of other attack methods that a firewall can thwart. There is more to firewalls than just blocking and allowing ports.
I can't speak much about IDS.
Source: I have experience setting up firewall/gateways on FreeBSD in IPv4 and IPv6 environments.