There's no single correct answer to this, because choosing the cipher suites must be a suitable compromise between security and compatibility. The Mozilla's Server Side TLS Guidelines linked on the configuration generator explains the purpose for the different profiles:
Modern compatibility. For services that don't need backward compatibility, the parameters below provide a higher level of
security. This configuration is compatible with Firefox 27, Chrome 30,
IE 11 on Windows 7, Edge, Opera 17, Safari 9, Android 5.0, and Java 8.
Intermediate compatibility (default). For services that don't need compatibility with legacy clients (mostly WinXP), but still need
to support a wide range of clients, this configuration is recommended.
It is is compatible with Firefox 1, Chrome 1, IE 7, Opera 5 and Safari
Old backward compatibility. This is the old ciphersuite that works with all clients back to Windows XP/IE6. It should be used as a
last resort only.
Adding TLS 1.3 to these recommendations has been under discussion, but hasn't yet been added. This reasoning is from 2016, before TLS 1.3 was proposed as a standard in RFC 8446:
jvehent on Dec 27, 2016 Contributor
I don't think we should recommend experimental versions here. We
waited for CHACHA20 to be standardized before adding it to the
guidelines, the same applies to TLS1.3.
Likewise, Qualys SSL Labs has published SSL and TLS Deployment Best Practices. As it was (as of Jun 2019) last updated in May 2017, it also mentions TLS 1.3 only as a future protocol, but it explains the problems with older versions prior TLS 1.2:
TLS v1.2 should be your main protocol because it's the only version
that offers modern authenticated encryption (also known as AEAD). If
you don't support TLS v1.2 today, your security is lacking.
In order to support older clients, you may need to continue to support
TLS v1.0 and TLS v1.1 for now. However, you should plan to retire TLS
v1.0 in the near future. For example, the PCI DSS standard will
require all sites that accept credit card payments to remove support
for TLS v1.0 by June 2018.
Work is currently under way to design TLS v1.3, with the aims to
remove all obsolete and insecure features and to make improvements
that will keep our communication secure in the following decades.
The SSL Labs Server Test is updated more regularly and points out additional possible weaknesses:
TLS_RSA ciphersuites have been marked as WEAK because they don't provide forward secrecy: if the private key gets compromised in the future, all recorded traffic can be decrypted using it.
- All ciphersuites utilizing Cipher Block Chaining
CBC aren't automatically weak, but there have been so many implementations vulnerable to padding oracle attacks that they have decided to mark them all as WEAK.
We also have a best current practice RFC 7525 from May 2015; Recommendations for Secure Use of Transport Layer Security (TLS) and Datagram Transport Layer Security (DTLS). Its section 4.2 gives recommendations that are similar to Mozilla's modern compatibility and SSL Labs Server Test:
Given the foregoing considerations, implementation and deployment
of the following cipher suites is RECOMMENDED:
These cipher suites are supported only in TLS 1.2 because they are
authenticated encryption (AEAD) algorithms [RFC5116].
Based on all this it might be just fine to "tweak to your needs" the modern profile by e.g.
- removing CBC based ciphersuites from the Modern compatibility profile i.e remove
- adding DHE ciphersuites as long as they have key length of at least 2048 bits and use GCM mode:
The Handshake Simulation section in SSL Labs Server Test helps pointing out the browsers that the configuration doesn't support. It's up to you to decide whether it's important to support them or not, and add the strongest ciphersuite available on that browser.
Whether to wait for Mozilla's recommendation on implementing TLS 1.3 or not is also opinion based. Good news for you is that TLS 1.3 has completely removed support for all legacy algorithms, making it harder to pick bad ciphersuites. From RFC 8446, 1.2. Major Differences from TLS 1.2:
The list of supported symmetric encryption algorithms has been
pruned of all algorithms that are considered legacy. Those that
remain are all Authenticated Encryption with Associated Data
(AEAD) algorithms. The cipher suite concept has been changed to
separate the authentication and key exchange mechanisms from the
record protection algorithm (including secret key length) and a
hash to be used with both the key derivation function and
handshake message authentication code (MAC).