Richard is right, you might be better thinking about how you can better use what you have already. The tower is probably at least as powerful as any laptop you would buy and the tower probably it isn't doing very much most of the time, so it seems a shame to waste its potential. All you really need is a way of connecting to it to tell it what you want it to do and see what it says on a screen. Without going back into the operating systems debate, most of the machines I use are (a) remote from me and (b) serving many other users simultaneously. Computers can do that sort of thing easily, it's only people like those who run Microsoft who will tell you "another user is logged onto this machine, if you continue they may lose their work". Microsoft deliberately cripples its software. I think that by now, the cost to British Industry of that, plus all the aggravation from botnets and viruses has far exceeded the cost of all the damage that the Luftwaffe ever did..
I use a laptop most of the time, but to me it's more or less just a screen and a keyboard. I can drive any of the other machines I use from the laptop just as if I were sitting next to the machines I'm driving. But they're spread all over the world, so it's physically impossible to sit next to them all at once. I just have a dozen or so windows open (most of them hidden, I don't like a cluttered screen) and when I want to take a peek at, say, my mailserver in Sheffield I just switch windows. These windows are 'X' windows by the way, not "Windows(TM)" windows.
You can set up your tower to be driven remotely. Look up "remote desktop". Then a very cheap, not very powerful PC can drive a more expensive powerful tower and you can have the best of both worlds for very little outlay.
Not sure what you mean by 'the signal is weak' but there are plenty of very easy ways to get around that. I'd recommend a wired (Ethernet) connection if at all possible. More secure, cheaper, faster (within the home LAN, you can easily do a thousand Megabits per second -- wireless will typically do 54 Megabits per second tops). The LAN speed starts to be important when you use 'remote desktop' and similar. Where possible I avoid it with my systems, you can too if you install something like Cygwin, but don't go there for now.