Generally speaking, if you’re talking colocation, it’s not worth it. The rates for colocation are set (deliberately, IMO) high enough that it’s literally no cheaper than leasing the entire box from that provider… and if you lease the whole box, they’re on the hook for maintenance and upgrades, whereas if you colo a box any problem you have is a problem you’re hoping the datacenter techs are feeling cooperative about, because there’s always the “this is your box, your problem, not our fault that whatever happened happened or we’re ‘having trouble’ repairing it, etc, etc.”
So basically, if you want to go this route, what you’re looking to do is rent a box from an inexpensive bare metal provider like (for example) PhoenixNAP or Hetzner. Hetzner is about half the cost of anybody else in the biz, but their network arrangement is… bizarre, at best, to the point that I really don’t recommend it for providing public-facing services that might require multiple IP addresses. But it’s fine if you only need a single public-facing IP, and you use eg WireGuard to connect to that.
PhoenixNAP is still inexpensive compared to most of the industry, but somewhere between half again as expensive and twice as expensive as Hetzner. But they give you a perfectly normal subnet that you can feed directly to the machine and, eg, set up a perfectly normal bridge adapter that you use to put VMs on public-facing IPs. Again, this may not be something you need, but it’s something to be aware of if you do.
How much does this kinda thing cost? Well, this server is on PhoenixNAP, and it runs me about $150/mo. That roughly $150/mo gets me a /29 IPv4 subnet (8 IP addresses, meaning 5 usable-by-me IP addresses after you deduct the network, broadcast, and gateway addresses) , 64GIB RAM, a Xeon E-2276G (6 cores / 12 threads at 3.1GHz), and two 1TB SSDs (one Intel NVMe, one Samsung 860 Pro).
I’ve got another customer at Hetzner with a pretty similar hardware loadout, and they’re paying about $90/mo as I recall… but I’m not kidding about how obnoxious that network setup at Hetzner is; I needed to run VMs there (as I do here; we’re actually operating on a VM on the bare metal host I described) and I ended up just saying to hell with public facing AT ALL, because that client was OK with just accessing their stuff via WireGuard to the host only.
Hope this helps.