OK, Jonny, that's good information for us to have. Because you have a little one on the way and are on a budget, I'd suggest that you narrow guns down to something that: (a) is suitable for home defense; and (b) can be carried concealed in the future. Buying one gun instead of two is cheaper and has the advantage that you only need to learn to operate one gun instead of two. I've picked up a saying from a buddy of mine, who is very knowledgeable about guns: "A gunfight is not the time to learn new techniques."
There are a whole list of guns that are suitable for both HD and CCW: Rugers, Glocks, S&Ws, Colts, just to name a few. That is by no means an exhaustive list.
As for the semi vs. revolver debate, . . . well, there are pros and cons to each one. You may well have considered all of the factors involved, but I'm going to lay out some pros and cons of each one, just to be sure that you're aware of them. These are very broad generalizations, and exceptions to them most certainly exist.
Semi-auto:
Pros:
1) Larger capacity
2) Potentially faster reloads
3) Slimmer profile (and thus easier to cc)
Cons:
1) More complicated manual of arms
2) Can be disabled by being pushed out of battery
3) In case of misfire or jams, a new round will need to be chambered or perhaps another magazine seated
Revolver:
Pros:
1) Simpler manual of arms
2) Cannot be pushed out of battery
3) In case of a misfire, just pull the trigger again
4) Jams (in the same sense that a semi might have one) seem very unlikely
Cons:
1) Wider profile
2) Potentially slower reloads
Also bear in mind that a semi auto may have a variety of safeties that a revolver doesn't have. I won't list this under the pros or cons, because it's sort of a "phantom con" on revolvers. By that I mean, the trigger pull on a DA revolver can be quite heavy, as compared to some semiautos, so you've got to really want to shoot the revolver for it to happen.
If you decide to go with a semi-auto, I'm going to recommend something in 9 mm. There are plenty of perfectly good 9 mm HD/SD rounds out there, and 9 mm is also a moderately priced round, so that you can afford to practice more than you would with a larger round, like the .45 acp.
I'm going to cast my vote with these other fellows who've suggested getting a .357 revolver and loading it with .38. A .357 revolver (not to be confused with .357 SIG semi-autos) will also shoot .38 ammunition. It's a moderately-priced round, so you can afford to practice more than you would be able to with a larger caliber. There's .38 ammunition out there that will work fine for HD, if you do your part. There's also fairly inexpensive .38 ammunition that will work for practice. You can also load it with .357 magnums if you choose, and they're also a fine HD round.